TSTP Solution File: SET812+4 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET812+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n013.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 00:22:14 EDT 2022
% Result : Theorem 7.98s 2.55s
% Output : Proof 11.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET812+4 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 07:17:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.59/0.60 ____ _
% 0.59/0.60 ___ / __ \_____(_)___ ________ __________
% 0.59/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.59/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.59/0.60
% 0.59/0.60 A Theorem Prover for First-Order Logic
% 0.59/0.61 (ePrincess v.1.0)
% 0.59/0.61
% 0.59/0.61 (c) Philipp Rümmer, 2009-2015
% 0.59/0.61 (c) Peter Backeman, 2014-2015
% 0.59/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.61 Bug reports to peter@backeman.se
% 0.59/0.61
% 0.59/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.61
% 0.59/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.64/0.99 Prover 0: Preprocessing ...
% 2.49/1.26 Prover 0: Warning: ignoring some quantifiers
% 2.49/1.29 Prover 0: Constructing countermodel ...
% 5.31/1.95 Prover 0: gave up
% 5.31/1.95 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.31/1.98 Prover 1: Preprocessing ...
% 6.28/2.11 Prover 1: Constructing countermodel ...
% 6.74/2.25 Prover 1: gave up
% 6.74/2.25 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.74/2.28 Prover 2: Preprocessing ...
% 7.57/2.40 Prover 2: Warning: ignoring some quantifiers
% 7.57/2.41 Prover 2: Constructing countermodel ...
% 7.98/2.55 Prover 2: proved (297ms)
% 7.98/2.55
% 7.98/2.55 No countermodel exists, formula is valid
% 7.98/2.55 % SZS status Theorem for theBenchmark
% 7.98/2.55
% 7.98/2.55 Generating proof ... Warning: ignoring some quantifiers
% 10.53/3.11 found it (size 70)
% 10.53/3.11
% 10.53/3.11 % SZS output start Proof for theBenchmark
% 10.53/3.11 Assumed formulas after preprocessing and simplification:
% 10.53/3.11 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection(v0, v1) = v2 & power_set(v0) = v1 & equal_set(v0, v2) = v3 & member(v0, on) = 0 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (initial_segment(v4, v5, v6) = v8) | ~ (member(v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & apply(v5, v7, v4) = v10) | ( ~ (v10 = 0) & member(v7, v6) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apply(v4, v7, v8) = 0) | ~ (apply(v4, v6, v8) = v9) | ~ (strict_order(v4, v5) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v4, v6, v7) = v10) | ( ~ (v10 = 0) & member(v8, v5) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apply(v4, v6, v8) = v9) | ~ (apply(v4, v6, v7) = 0) | ~ (strict_order(v4, v5) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v4, v7, v8) = v10) | ( ~ (v10 = 0) & member(v8, v5) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10) | ( ~ (v10 = 0) & member(v6, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apply(v4, v6, v8) = v9) | ~ (strict_order(v4, v5) = 0) | ~ (member(v7, v5) = 0) | ? [v10] : (( ~ (v10 = 0) & apply(v4, v7, v8) = v10) | ( ~ (v10 = 0) & apply(v4, v6, v7) = v10) | ( ~ (v10 = 0) & member(v8, v5) = v10) | ( ~ (v10 = 0) & member(v6, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = v6 | ~ (apply(v4, v6, v7) = v8) | ~ (least(v6, v4, v5) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (product(v5) = v6) | ~ (member(v4, v7) = v8) | ~ (member(v4, v6) = 0) | ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (singleton(v4) = v6) | ~ (union(v4, v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & suc(v4) = v9 & member(v5, v9) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (difference(v6, v5) = v7) | ~ (member(v4, v7) = v8) | ? [v9] : ((v9 = 0 & member(v4, v5) = 0) | ( ~ (v9 = 0) & member(v4, v6) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (union(v5, v6) = v7) | ~ (member(v4, v7) = v8) | ? [v9] : ? [v10] : ( ~ (v10 = 0) & ~ (v9 = 0) & member(v4, v6) = v10 & member(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (intersection(v5, v6) = v7) | ~ (member(v4, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & member(v4, v6) = v9) | ( ~ (v9 = 0) & member(v4, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (sum(v5) = v6) | ~ (member(v8, v5) = 0) | ~ (member(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & member(v4, v8) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = 0 | ~ (sum(v5) = v6) | ~ (member(v4, v8) = 0) | ~ (member(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & member(v8, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (initial_segment(v8, v7, v6) = v5) | ~ (initial_segment(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (apply(v8, v7, v6) = v5) | ~ (apply(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (least(v8, v7, v6) = v5) | ~ (least(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (initial_segment(v4, v5, v6) = v8) | ~ (member(v7, v8) = 0) | (apply(v5, v7, v4) = 0 & member(v7, v6) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v4, v7, v8) = 0) | ~ (apply(v4, v6, v7) = 0) | ~ (strict_order(v4, v5) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & member(v8, v5) = v9) | ( ~ (v9 = 0) & member(v7, v5) = v9) | ( ~ (v9 = 0) & member(v6, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v4, v7, v8) = 0) | ~ (strict_order(v4, v5) = 0) | ~ (member(v6, v5) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v4, v6, v7) = v9) | ( ~ (v9 = 0) & member(v8, v5) = v9) | ( ~ (v9 = 0) & member(v7, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (apply(v4, v6, v7) = 0) | ~ (strict_order(v4, v5) = 0) | ~ (member(v8, v5) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v4, v7, v8) = v9) | ( ~ (v9 = 0) & member(v7, v5) = v9) | ( ~ (v9 = 0) & member(v6, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (strict_order(v4, v5) = v6) | ~ (subset(v7, v5) = 0) | ~ (member(v8, v7) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & least(v9, v4, v7) = 0) | ( ~ (v9 = 0) & strict_well_order(v4, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (strict_order(v4, v5) = 0) | ~ (member(v8, v5) = 0) | ~ (member(v7, v5) = 0) | ~ (member(v6, v5) = 0) | ? [v9] : ((v9 = 0 & apply(v4, v6, v8) = 0) | ( ~ (v9 = 0) & apply(v4, v7, v8) = v9) | ( ~ (v9 = 0) & apply(v4, v6, v7) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (least(v6, v4, v5) = 0) | ~ (member(v7, v5) = 0) | apply(v4, v6, v7) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (suc(v4) = v6) | ~ (member(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & singleton(v4) = v8 & union(v4, v8) = v9 & member(v5, v9) = v10)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (least(v6, v4, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v9 = 0 & ~ (v10 = 0) & ~ (v8 = v6) & apply(v4, v6, v8) = v10 & member(v8, v5) = 0) | ( ~ (v8 = 0) & member(v6, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (product(v5) = v6) | ~ (member(v4, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & member(v8, v5) = 0 & member(v4, v8) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unordered_pair(v5, v4) = v6) | ~ (member(v4, v6) = v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unordered_pair(v4, v5) = v6) | ~ (member(v4, v6) = v7)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (power_set(v5) = v6) | ~ (member(v4, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & subset(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v4, v5) = 0) | ~ (member(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & member(v6, v4) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = v4 | v5 = v4 | ~ (unordered_pair(v5, v6) = v7) | ~ (member(v4, v7) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (strict_order(v7, v6) = v5) | ~ (strict_order(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (strict_well_order(v7, v6) = v5) | ~ (strict_well_order(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (unordered_pair(v7, v6) = v5) | ~ (unordered_pair(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (difference(v7, v6) = v5) | ~ (difference(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (union(v7, v6) = v5) | ~ (union(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (intersection(v7, v6) = v5) | ~ (intersection(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equal_set(v7, v6) = v5) | ~ (equal_set(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (subset(v7, v6) = v5) | ~ (subset(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (member(v7, v6) = v5) | ~ (member(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v4, v7, v6) = 0) | ~ (strict_order(v4, v5) = 0) | ? [v8] : (( ~ (v8 = 0) & apply(v4, v6, v7) = v8) | ( ~ (v8 = 0) & member(v7, v5) = v8) | ( ~ (v8 = 0) & member(v6, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v4, v6, v7) = 0) | ~ (strict_order(v4, v5) = 0) | ? [v8] : (( ~ (v8 = 0) & apply(v4, v7, v6) = v8) | ( ~ (v8 = 0) & member(v7, v5) = v8) | ( ~ (v8 = 0) & member(v6, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (strict_well_order(v4, v5) = 0) | ~ (subset(v6, v5) = 0) | ~ (member(v7, v6) = 0) | ? [v8] : least(v8, v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (product(v5) = v6) | ~ (member(v7, v5) = 0) | ~ (member(v4, v6) = 0) | member(v4, v7) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (singleton(v4) = v6) | ~ (union(v4, v6) = v7) | ~ (member(v5, v7) = 0) | ? [v8] : (suc(v4) = v8 & member(v5, v8) = 0)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (difference(v6, v5) = v7) | ~ (member(v4, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v4, v6) = 0 & member(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v5, v6) = v7) | ~ (member(v4, v7) = 0) | ? [v8] : ((v8 = 0 & member(v4, v6) = 0) | (v8 = 0 & member(v4, v5) = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection(v5, v6) = v7) | ~ (member(v4, v7) = 0) | (member(v4, v6) = 0 & member(v4, v5) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (apply(member_predicate, v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & member(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (strict_order(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v14 = 0 & v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & ~ (v15 = 0) & apply(v4, v8, v9) = 0 & apply(v4, v7, v9) = v15 & apply(v4, v7, v8) = 0 & member(v9, v5) = 0 & member(v8, v5) = 0 & member(v7, v5) = 0) | (v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & apply(v4, v8, v7) = 0 & apply(v4, v7, v8) = 0 & member(v8, v5) = 0 & member(v7, v5) = 0))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (strict_order(v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & strict_well_order(v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (strict_well_order(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = 0 & subset(v7, v5) = 0 & member(v9, v7) = 0 & ! [v11] : ~ (least(v11, v4, v7) = 0)) | ( ~ (v7 = 0) & strict_order(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (set(v5) = v6) | ~ (set(v4) = 0) | ? [v7] : ( ~ (v7 = 0) & member(v5, v4) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (singleton(v4) = v5) | ~ (member(v4, v5) = v6)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equal_set(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & subset(v5, v4) = v7) | ( ~ (v7 = 0) & subset(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v5, v4) = v6) | ~ (member(v4, on) = 0) | ? [v7] : ( ~ (v7 = 0) & member(v5, v4) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & power_set(v5) = v7 & member(v4, v7) = v8)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & member(v7, v5) = v8 & member(v7, v4) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (member(v4, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & apply(member_predicate, v4, v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (suc(v6) = v5) | ~ (suc(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (set(v6) = v5) | ~ (set(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (product(v6) = v5) | ~ (product(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (sum(v6) = v5) | ~ (sum(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (singleton(v6) = v5) | ~ (singleton(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (singleton(v5) = v6) | ~ (member(v4, v6) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (power_set(v6) = v5) | ~ (power_set(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (suc(v4) = v6) | ~ (member(v5, v6) = 0) | ? [v7] : ? [v8] : (singleton(v4) = v7 & union(v4, v7) = v8 & member(v5, v8) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (least(v6, v4, v5) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (sum(v5) = v6) | ~ (member(v4, v6) = 0) | ? [v7] : (member(v7, v5) = 0 & member(v4, v7) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (power_set(v5) = v6) | ~ (member(v4, v6) = 0) | subset(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (subset(v5, v4) = v6) | ? [v7] : ((v7 = 0 & v6 = 0 & subset(v4, v5) = 0) | ( ~ (v7 = 0) & equal_set(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (subset(v4, v5) = v6) | ? [v7] : ((v7 = 0 & v6 = 0 & subset(v5, v4) = 0) | ( ~ (v7 = 0) & equal_set(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (subset(v4, v5) = 0) | ~ (member(v6, v4) = 0) | member(v6, v5) = 0) & ! [v4] : ! [v5] : (v5 = 0 | ~ (member(v4, on) = v5) | ? [v6] : ? [v7] : ? [v8] : ((v7 = 0 & ~ (v8 = 0) & subset(v6, v4) = v8 & member(v6, v4) = 0) | ( ~ (v6 = 0) & strict_well_order(member_predicate, v4) = v6) | ( ~ (v6 = 0) & set(v4) = v6))) & ! [v4] : ! [v5] : ( ~ (apply(member_predicate, v4, v5) = 0) | member(v4, v5) = 0) & ! [v4] : ! [v5] : ( ~ (strict_order(v4, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v7 = 0 & subset(v6, v5) = 0 & member(v8, v6) = 0 & ! [v10] : ~ (least(v10, v4, v6) = 0)) | (v6 = 0 & strict_well_order(v4, v5) = 0))) & ! [v4] : ! [v5] : ( ~ (strict_well_order(v4, v5) = 0) | strict_order(v4, v5) = 0) & ! [v4] : ! [v5] : ( ~ (strict_well_order(member_predicate, v4) = v5) | ? [v6] : ((v6 = 0 & v5 = 0 & set(v4) = 0 & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v4) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v4) = v9)) & ! [v7] : ( ~ (member(v7, v4) = 0) | subset(v7, v4) = 0)) | ( ~ (v6 = 0) & member(v4, on) = v6))) & ! [v4] : ! [v5] : ( ~ (set(v4) = v5) | ? [v6] : ((v6 = 0 & v5 = 0 & strict_well_order(member_predicate, v4) = 0 & ! [v7] : ! [v8] : (v8 = 0 | ~ (subset(v7, v4) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v7, v4) = v9)) & ! [v7] : ( ~ (member(v7, v4) = 0) | subset(v7, v4) = 0)) | ( ~ (v6 = 0) & member(v4, on) = v6))) & ! [v4] : ! [v5] : ( ~ (set(v4) = 0) | ~ (member(v5, v4) = 0) | set(v5) = 0) & ! [v4] : ! [v5] : ( ~ (equal_set(v4, v5) = 0) | (subset(v5, v4) = 0 & subset(v4, v5) = 0)) & ! [v4] : ! [v5] : ( ~ (subset(v5, v4) = 0) | ? [v6] : ((v6 = 0 & equal_set(v4, v5) = 0) | ( ~ (v6 = 0) & subset(v4, v5) = v6))) & ! [v4] : ! [v5] : ( ~ (subset(v4, v5) = 0) | ? [v6] : (power_set(v5) = v6 & member(v4, v6) = 0)) & ! [v4] : ! [v5] : ( ~ (subset(v4, v5) = 0) | ? [v6] : ((v6 = 0 & equal_set(v4, v5) = 0) | ( ~ (v6 = 0) & subset(v5, v4) = v6))) & ! [v4] : ! [v5] : ( ~ (member(v5, v4) = 0) | ~ (member(v4, on) = 0) | subset(v5, v4) = 0) & ! [v4] : ! [v5] : ( ~ (member(v4, v5) = 0) | apply(member_predicate, v4, v5) = 0) & ! [v4] : ( ~ (strict_well_order(member_predicate, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & ~ (v7 = 0) & subset(v5, v4) = v7 & member(v5, v4) = 0) | (v5 = 0 & member(v4, on) = 0) | ( ~ (v5 = 0) & set(v4) = v5))) & ! [v4] : ( ~ (set(v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & ~ (v7 = 0) & subset(v5, v4) = v7 & member(v5, v4) = 0) | (v5 = 0 & member(v4, on) = 0) | ( ~ (v5 = 0) & strict_well_order(member_predicate, v4) = v5))) & ! [v4] : ( ~ (member(v4, on) = 0) | (strict_well_order(member_predicate, v4) = 0 & set(v4) = 0)) & ! [v4] : ~ (member(v4, empty_set) = 0) & ? [v4] : ? [v5] : ? [v6] : ? [v7] : initial_segment(v6, v5, v4) = v7 & ? [v4] : ? [v5] : ? [v6] : ? [v7] : apply(v6, v5, v4) = v7 & ? [v4] : ? [v5] : ? [v6] : ? [v7] : least(v6, v5, v4) = v7 & ? [v4] : ? [v5] : ? [v6] : strict_order(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : strict_well_order(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : unordered_pair(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : difference(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : union(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : intersection(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : equal_set(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : subset(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : member(v5, v4) = v6 & ? [v4] : ? [v5] : suc(v4) = v5 & ? [v4] : ? [v5] : set(v4) = v5 & ? [v4] : ? [v5] : product(v4) = v5 & ? [v4] : ? [v5] : sum(v4) = v5 & ? [v4] : ? [v5] : singleton(v4) = v5 & ? [v4] : ? [v5] : power_set(v4) = v5)
% 10.53/3.16 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 10.53/3.16 | (1) ~ (all_0_0_0 = 0) & intersection(all_0_3_3, all_0_2_2) = all_0_1_1 & power_set(all_0_3_3) = all_0_2_2 & equal_set(all_0_3_3, all_0_1_1) = all_0_0_0 & member(all_0_3_3, on) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (initial_segment(v0, v1, v2) = v4) | ~ (member(v3, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & apply(v1, v3, v0) = v6) | ( ~ (v6 = 0) & member(v3, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apply(v0, v3, v4) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (strict_order(v0, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (strict_order(v0, v1) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = v2 | ~ (apply(v0, v2, v3) = v4) | ~ (least(v2, v0, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (singleton(v0) = v2) | ~ (union(v0, v2) = v3) | ~ (member(v1, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & suc(v0) = v5 & member(v1, v5) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (initial_segment(v4, v3, v2) = v1) | ~ (initial_segment(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (initial_segment(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | (apply(v1, v3, v0) = 0 & member(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v0, v3, v4) = 0) | ~ (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & member(v4, v1) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5) | ( ~ (v5 = 0) & member(v2, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v0, v3, v4) = 0) | ~ (strict_order(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v2, v3) = v5) | ( ~ (v5 = 0) & member(v4, v1) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ~ (member(v4, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v3, v4) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5) | ( ~ (v5 = 0) & member(v2, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (strict_order(v0, v1) = v2) | ~ (subset(v3, v1) = 0) | ~ (member(v4, v3) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & least(v5, v0, v3) = 0) | ( ~ (v5 = 0) & strict_well_order(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (strict_order(v0, v1) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v3, v4) = v5) | ( ~ (v5 = 0) & apply(v0, v2, v3) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (least(v2, v0, v1) = 0) | ~ (member(v3, v1) = 0) | apply(v0, v2, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (suc(v0) = v2) | ~ (member(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & singleton(v0) = v4 & union(v0, v4) = v5 & member(v1, v5) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (least(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & ~ (v4 = v2) & apply(v0, v2, v4) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strict_order(v3, v2) = v1) | ~ (strict_order(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strict_well_order(v3, v2) = v1) | ~ (strict_well_order(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 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apply(v0, v3, v2) = 0) | ~ (strict_order(v0, v1) = 0) | ? [v4] : (( ~ (v4 = 0) & apply(v0, v2, v3) = v4) | ( ~ (v4 = 0) & member(v3, v1) = v4) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ? [v4] : (( ~ (v4 = 0) & apply(v0, v3, v2) = v4) | ( ~ (v4 = 0) & member(v3, v1) = v4) | ( ~ (v4 = 0) & member(v2, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strict_well_order(v0, v1) = 0) | ~ (subset(v2, v1) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : least(v4, v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (singleton(v0) = v2) | ~ (union(v0, v2) = v3) | ~ (member(v1, v3) = 0) | ? [v4] : (suc(v0) = v4 & member(v1, v4) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apply(member_predicate, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & member(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strict_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & apply(v0, v4, v3) = 0 & apply(v0, v3, v4) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strict_order(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & strict_well_order(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strict_well_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & subset(v3, v1) = 0 & member(v5, v3) = 0 & ! [v7] : ~ (least(v7, v0, v3) = 0)) | ( ~ (v3 = 0) & strict_order(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (set(v1) = v2) | ~ (set(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v0) = v2) | ~ (member(v0, on) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (member(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & apply(member_predicate, v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (suc(v2) = v1) | ~ (suc(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set(v2) = v1) | ~ (set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (suc(v0) = v2) | ~ (member(v1, v2) = 0) | ? [v3] : ? [v4] : (singleton(v0) = v3 & union(v0, v3) = v4 & member(v1, v4) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : (v1 = 0 | ~ (member(v0, on) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & subset(v2, v0) = v4 & member(v2, v0) = 0) | ( ~ (v2 = 0) & strict_well_order(member_predicate, v0) = v2) | ( ~ (v2 = 0) & set(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (apply(member_predicate, v0, v1) = 0) | member(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (strict_order(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & subset(v2, v1) = 0 & member(v4, v2) = 0 & ! [v6] : ~ (least(v6, v0, v2) = 0)) | (v2 = 0 & strict_well_order(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (strict_well_order(v0, v1) = 0) | strict_order(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (strict_well_order(member_predicate, v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & set(v0) = 0 & ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v0) = v5)) & ! [v3] : ( ~ (member(v3, v0) = 0) | subset(v3, v0) = 0)) | ( ~ (v2 = 0) & member(v0, on) = v2))) & ! [v0] : ! [v1] : ( ~ (set(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & strict_well_order(member_predicate, v0) = 0 & ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v0) = v5)) & ! [v3] : ( ~ (member(v3, v0) = 0) | subset(v3, v0) = 0)) | ( ~ (v2 = 0) & member(v0, on) = v2))) & ! [v0] : ! [v1] : ( ~ (set(v0) = 0) | ~ (member(v1, v0) = 0) | set(v1) = 0) & ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2))) & ! [v0] : ! [v1] : ( ~ (member(v1, v0) = 0) | ~ (member(v0, on) = 0) | subset(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (member(v0, v1) = 0) | apply(member_predicate, v0, v1) = 0) & ! [v0] : ( ~ (strict_well_order(member_predicate, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & ~ (v3 = 0) & subset(v1, v0) = v3 & member(v1, v0) = 0) | (v1 = 0 & member(v0, on) = 0) | ( ~ (v1 = 0) & set(v0) = v1))) & ! [v0] : ( ~ (set(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & ~ (v3 = 0) & subset(v1, v0) = v3 & member(v1, v0) = 0) | (v1 = 0 & member(v0, on) = 0) | ( ~ (v1 = 0) & strict_well_order(member_predicate, v0) = v1))) & ! [v0] : ( ~ (member(v0, on) = 0) | (strict_well_order(member_predicate, v0) = 0 & set(v0) = 0)) & ! [v0] : ~ (member(v0, empty_set) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : initial_segment(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : least(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : strict_order(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : strict_well_order(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 & ? [v0] : ? [v1] : suc(v0) = v1 & ? [v0] : ? [v1] : set(v0) = v1 & ? [v0] : ? [v1] : product(v0) = v1 & ? [v0] : ? [v1] : sum(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : ? [v1] : power_set(v0) = v1
% 10.98/3.19 |
% 10.98/3.19 | Applying alpha-rule on (1) yields:
% 10.98/3.19 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set(v2) = v1) | ~ (set(v2) = v0))
% 10.98/3.19 | (3) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strict_well_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & subset(v3, v1) = 0 & member(v5, v3) = 0 & ! [v7] : ~ (least(v7, v0, v3) = 0)) | ( ~ (v3 = 0) & strict_order(v0, v1) = v3)))
% 10.98/3.19 | (4) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 11.09/3.19 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 11.09/3.19 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (singleton(v0) = v2) | ~ (union(v0, v2) = v3) | ~ (member(v1, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & suc(v0) = v5 & member(v1, v5) = v6))
% 11.09/3.19 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 11.09/3.19 | (8) power_set(all_0_3_3) = all_0_2_2
% 11.09/3.19 | (9) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 11.09/3.19 | (10) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 11.09/3.19 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6)))
% 11.09/3.19 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (member(v0, on) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v3 = 0 & ~ (v4 = 0) & subset(v2, v0) = v4 & member(v2, v0) = 0) | ( ~ (v2 = 0) & strict_well_order(member_predicate, v0) = v2) | ( ~ (v2 = 0) & set(v0) = v2)))
% 11.09/3.20 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = v2 | ~ (apply(v0, v2, v3) = v4) | ~ (least(v2, v0, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 11.09/3.20 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (singleton(v0) = v2) | ~ (union(v0, v2) = v3) | ~ (member(v1, v3) = 0) | ? [v4] : (suc(v0) = v4 & member(v1, v4) = 0))
% 11.09/3.20 | (15) member(all_0_3_3, on) = 0
% 11.09/3.20 | (16) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 11.09/3.20 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 11.09/3.20 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 11.09/3.20 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 11.09/3.20 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 11.09/3.20 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 11.09/3.20 | (22) ? [v0] : ? [v1] : ? [v2] : strict_well_order(v1, v0) = v2
% 11.09/3.20 | (23) ! [v0] : ~ (member(v0, empty_set) = 0)
% 11.09/3.20 | (24) equal_set(all_0_3_3, all_0_1_1) = all_0_0_0
% 11.09/3.20 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 11.09/3.20 | (26) ! [v0] : ! [v1] : ( ~ (member(v1, v0) = 0) | ~ (member(v0, on) = 0) | subset(v1, v0) = 0)
% 11.09/3.20 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5))
% 11.09/3.20 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (least(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & ~ (v4 = v2) & apply(v0, v2, v4) = v6 & member(v4, v1) = 0) | ( ~ (v4 = 0) & member(v2, v1) = v4)))
% 11.09/3.20 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 11.09/3.20 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (initial_segment(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | (apply(v1, v3, v0) = 0 & member(v3, v2) = 0))
% 11.09/3.20 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 11.09/3.20 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 11.09/3.20 | (33) ~ (all_0_0_0 = 0)
% 11.09/3.20 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 11.09/3.20 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (initial_segment(v4, v3, v2) = v1) | ~ (initial_segment(v4, v3, v2) = v0))
% 11.09/3.20 | (36) ? [v0] : ? [v1] : singleton(v0) = v1
% 11.09/3.20 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 11.09/3.20 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ((v5 = 0 & member(v0, v1) = 0) | ( ~ (v5 = 0) & member(v0, v2) = v5)))
% 11.09/3.20 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 11.09/3.20 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strict_order(v3, v2) = v1) | ~ (strict_order(v3, v2) = v0))
% 11.09/3.20 | (41) ? [v0] : ? [v1] : sum(v0) = v1
% 11.09/3.20 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (member(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & apply(member_predicate, v0, v1) = v3))
% 11.09/3.20 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apply(member_predicate, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & member(v0, v1) = v3))
% 11.09/3.20 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0))
% 11.09/3.20 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 11.09/3.20 | (46) ? [v0] : ? [v1] : set(v0) = v1
% 11.09/3.20 | (47) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3
% 11.09/3.20 | (48) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 11.09/3.20 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (suc(v0) = v2) | ~ (member(v1, v2) = 0) | ? [v3] : ? [v4] : (singleton(v0) = v3 & union(v0, v3) = v4 & member(v1, v4) = 0))
% 11.09/3.20 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 11.09/3.20 | (51) ? [v0] : ? [v1] : power_set(v0) = v1
% 11.09/3.20 | (52) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strict_order(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & strict_well_order(v0, v1) = v3))
% 11.09/3.20 | (53) ? [v0] : ? [v1] : product(v0) = v1
% 11.09/3.20 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = v5))
% 11.09/3.20 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (suc(v0) = v2) | ~ (member(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = 0) & singleton(v0) = v4 & union(v0, v4) = v5 & member(v1, v5) = v6))
% 11.09/3.20 | (56) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 11.09/3.20 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 11.09/3.20 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 11.09/3.20 | (59) ! [v0] : ! [v1] : ( ~ (set(v0) = 0) | ~ (member(v1, v0) = 0) | set(v1) = 0)
% 11.09/3.20 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 11.09/3.20 | (61) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 11.09/3.20 | (62) ! [v0] : ! [v1] : ( ~ (set(v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & strict_well_order(member_predicate, v0) = 0 & ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v0) = v5)) & ! [v3] : ( ~ (member(v3, v0) = 0) | subset(v3, v0) = 0)) | ( ~ (v2 = 0) & member(v0, on) = v2)))
% 11.09/3.20 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 11.09/3.20 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (strict_order(v0, v1) = v2) | ~ (subset(v3, v1) = 0) | ~ (member(v4, v3) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & least(v5, v0, v3) = 0) | ( ~ (v5 = 0) & strict_well_order(v0, v1) = v5)))
% 11.09/3.20 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (least(v2, v0, v1) = 0) | ~ (member(v3, v1) = 0) | apply(v0, v2, v3) = 0)
% 11.09/3.20 | (66) ! [v0] : ( ~ (set(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & ~ (v3 = 0) & subset(v1, v0) = v3 & member(v1, v0) = 0) | (v1 = 0 & member(v0, on) = 0) | ( ~ (v1 = 0) & strict_well_order(member_predicate, v0) = v1)))
% 11.09/3.20 | (67) ! [v0] : ( ~ (strict_well_order(member_predicate, v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v2 = 0 & ~ (v3 = 0) & subset(v1, v0) = v3 & member(v1, v0) = 0) | (v1 = 0 & member(v0, on) = 0) | ( ~ (v1 = 0) & set(v0) = v1)))
% 11.09/3.20 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v3) = v4) | ~ (member(v0, v2) = 0) | ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 11.09/3.20 | (69) ? [v0] : ? [v1] : ? [v2] : strict_order(v1, v0) = v2
% 11.09/3.20 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v0, v3, v4) = 0) | ~ (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & member(v4, v1) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5) | ( ~ (v5 = 0) & member(v2, v1) = v5)))
% 11.09/3.21 | (71) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 11.09/3.21 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (product(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = 0 & member(v0, v4) = v5))
% 11.09/3.21 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (initial_segment(v0, v1, v2) = v4) | ~ (member(v3, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & apply(v1, v3, v0) = v6) | ( ~ (v6 = 0) & member(v3, v2) = v6)))
% 11.09/3.21 | (74) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strict_order(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & apply(v0, v4, v3) = 0 & apply(v0, v3, v4) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0)))
% 11.09/3.21 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strict_well_order(v0, v1) = 0) | ~ (subset(v2, v1) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : least(v4, v0, v2) = 0)
% 11.09/3.21 | (76) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 11.09/3.21 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ? [v4] : (( ~ (v4 = 0) & apply(v0, v3, v2) = v4) | ( ~ (v4 = 0) & member(v3, v1) = v4) | ( ~ (v4 = 0) & member(v2, v1) = v4)))
% 11.09/3.21 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (apply(v0, v3, v2) = 0) | ~ (strict_order(v0, v1) = 0) | ? [v4] : (( ~ (v4 = 0) & apply(v0, v2, v3) = v4) | ( ~ (v4 = 0) & member(v3, v1) = v4) | ( ~ (v4 = 0) & member(v2, v1) = v4)))
% 11.09/3.21 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 11.09/3.21 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v0, v2) = v5) | ( ~ (v5 = 0) & member(v0, v1) = v5)))
% 11.09/3.21 | (81) ? [v0] : ? [v1] : suc(v0) = v1
% 11.09/3.21 | (82) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 11.09/3.21 | (83) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 11.09/3.21 | (84) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 11.09/3.21 | (85) intersection(all_0_3_3, all_0_2_2) = all_0_1_1
% 11.09/3.21 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apply(v0, v3, v4) = 0) | ~ (apply(v0, v2, v4) = v5) | ~ (strict_order(v0, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v3, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6)))
% 11.09/3.21 | (87) ! [v0] : ( ~ (member(v0, on) = 0) | (strict_well_order(member_predicate, v0) = 0 & set(v0) = 0))
% 11.09/3.21 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~ (strict_order(v0, v1) = 0) | ~ (member(v3, v1) = 0) | ? [v6] : (( ~ (v6 = 0) & apply(v0, v3, v4) = v6) | ( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v6 = 0) & member(v4, v1) = v6) | ( ~ (v6 = 0) & member(v2, v1) = v6)))
% 11.09/3.21 | (89) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v0) = v2) | ~ (member(v0, on) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3))
% 11.09/3.21 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (strict_order(v0, v1) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v3, v4) = v5) | ( ~ (v5 = 0) & apply(v0, v2, v3) = v5)))
% 11.09/3.21 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v0, v3, v4) = 0) | ~ (strict_order(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v2, v3) = v5) | ( ~ (v5 = 0) & member(v4, v1) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5)))
% 11.09/3.21 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strict_well_order(v3, v2) = v1) | ~ (strict_well_order(v3, v2) = v0))
% 11.09/3.21 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 11.09/3.21 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5))
% 11.09/3.21 | (95) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (set(v1) = v2) | ~ (set(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3))
% 11.09/3.21 | (96) ! [v0] : ! [v1] : ( ~ (strict_well_order(v0, v1) = 0) | strict_order(v0, v1) = 0)
% 11.09/3.21 | (97) ! [v0] : ! [v1] : ( ~ (member(v0, v1) = 0) | apply(member_predicate, v0, v1) = 0)
% 11.09/3.21 | (98) ! [v0] : ! [v1] : ( ~ (apply(member_predicate, v0, v1) = 0) | member(v0, v1) = 0)
% 11.09/3.21 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ((v4 = 0 & member(v0, v2) = 0) | (v4 = 0 & member(v0, v1) = 0)))
% 11.09/3.21 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ~ (member(v4, v1) = 0) | ? [v5] : ((v5 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v5 = 0) & apply(v0, v3, v4) = v5) | ( ~ (v5 = 0) & member(v3, v1) = v5) | ( ~ (v5 = 0) & member(v2, v1) = v5)))
% 11.09/3.21 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 11.09/3.21 | (102) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 11.09/3.21 | (103) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 11.09/3.21 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 11.09/3.21 | (105) ? [v0] : ? [v1] : ? [v2] : ? [v3] : initial_segment(v2, v1, v0) = v3
% 11.09/3.21 | (106) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (suc(v2) = v1) | ~ (suc(v2) = v0))
% 11.09/3.21 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 11.09/3.21 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 11.09/3.21 | (109) ! [v0] : ! [v1] : ( ~ (strict_well_order(member_predicate, v0) = v1) | ? [v2] : ((v2 = 0 & v1 = 0 & set(v0) = 0 & ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & member(v3, v0) = v5)) & ! [v3] : ( ~ (member(v3, v0) = 0) | subset(v3, v0) = 0)) | ( ~ (v2 = 0) & member(v0, on) = v2)))
% 11.09/3.21 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 11.09/3.21 | (111) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 11.09/3.21 | (112) ? [v0] : ? [v1] : ? [v2] : ? [v3] : least(v2, v1, v0) = v3
% 11.09/3.21 | (113) ! [v0] : ! [v1] : ( ~ (strict_order(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & v3 = 0 & subset(v2, v1) = 0 & member(v4, v2) = 0 & ! [v6] : ~ (least(v6, v0, v2) = 0)) | (v2 = 0 & strict_well_order(v0, v1) = 0)))
% 11.09/3.21 |
% 11.09/3.21 | Instantiating formula (31) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms equal_set(all_0_3_3, all_0_1_1) = all_0_0_0, yields:
% 11.09/3.21 | (114) all_0_0_0 = 0 | ? [v0] : (( ~ (v0 = 0) & subset(all_0_1_1, all_0_3_3) = v0) | ( ~ (v0 = 0) & subset(all_0_3_3, all_0_1_1) = v0))
% 11.09/3.21 |
% 11.09/3.21 | Instantiating formula (87) with all_0_3_3 and discharging atoms member(all_0_3_3, on) = 0, yields:
% 11.09/3.21 | (115) strict_well_order(member_predicate, all_0_3_3) = 0 & set(all_0_3_3) = 0
% 11.09/3.21 |
% 11.09/3.21 | Applying alpha-rule on (115) yields:
% 11.09/3.21 | (116) strict_well_order(member_predicate, all_0_3_3) = 0
% 11.09/3.21 | (117) set(all_0_3_3) = 0
% 11.09/3.21 |
% 11.09/3.21 +-Applying beta-rule and splitting (114), into two cases.
% 11.09/3.21 |-Branch one:
% 11.09/3.21 | (118) all_0_0_0 = 0
% 11.09/3.21 |
% 11.09/3.21 | Equations (118) can reduce 33 to:
% 11.09/3.21 | (119) $false
% 11.09/3.21 |
% 11.09/3.22 |-The branch is then unsatisfiable
% 11.09/3.22 |-Branch two:
% 11.09/3.22 | (33) ~ (all_0_0_0 = 0)
% 11.09/3.22 | (121) ? [v0] : (( ~ (v0 = 0) & subset(all_0_1_1, all_0_3_3) = v0) | ( ~ (v0 = 0) & subset(all_0_3_3, all_0_1_1) = v0))
% 11.09/3.22 |
% 11.09/3.22 | Instantiating (121) with all_49_0_55 yields:
% 11.09/3.22 | (122) ( ~ (all_49_0_55 = 0) & subset(all_0_1_1, all_0_3_3) = all_49_0_55) | ( ~ (all_49_0_55 = 0) & subset(all_0_3_3, all_0_1_1) = all_49_0_55)
% 11.09/3.22 |
% 11.09/3.22 | Instantiating formula (109) with 0, all_0_3_3 and discharging atoms strict_well_order(member_predicate, all_0_3_3) = 0, yields:
% 11.09/3.22 | (123) ? [v0] : ((v0 = 0 & set(all_0_3_3) = 0 & ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, all_0_3_3) = v2) | ? [v3] : ( ~ (v3 = 0) & member(v1, all_0_3_3) = v3)) & ! [v1] : ( ~ (member(v1, all_0_3_3) = 0) | subset(v1, all_0_3_3) = 0)) | ( ~ (v0 = 0) & member(all_0_3_3, on) = v0))
% 11.09/3.22 |
% 11.09/3.22 | Instantiating (123) with all_57_0_57 yields:
% 11.09/3.22 | (124) (all_57_0_57 = 0 & set(all_0_3_3) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_0_3_3) = v1) | ? [v2] : ( ~ (v2 = 0) & member(v0, all_0_3_3) = v2)) & ! [v0] : ( ~ (member(v0, all_0_3_3) = 0) | subset(v0, all_0_3_3) = 0)) | ( ~ (all_57_0_57 = 0) & member(all_0_3_3, on) = all_57_0_57)
% 11.09/3.22 |
% 11.09/3.22 +-Applying beta-rule and splitting (124), into two cases.
% 11.09/3.22 |-Branch one:
% 11.09/3.22 | (125) all_57_0_57 = 0 & set(all_0_3_3) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_0_3_3) = v1) | ? [v2] : ( ~ (v2 = 0) & member(v0, all_0_3_3) = v2)) & ! [v0] : ( ~ (member(v0, all_0_3_3) = 0) | subset(v0, all_0_3_3) = 0)
% 11.09/3.22 |
% 11.09/3.22 | Applying alpha-rule on (125) yields:
% 11.09/3.22 | (126) all_57_0_57 = 0
% 11.20/3.22 | (117) set(all_0_3_3) = 0
% 11.20/3.22 | (128) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_0_3_3) = v1) | ? [v2] : ( ~ (v2 = 0) & member(v0, all_0_3_3) = v2))
% 11.20/3.22 | (129) ! [v0] : ( ~ (member(v0, all_0_3_3) = 0) | subset(v0, all_0_3_3) = 0)
% 11.20/3.22 |
% 11.20/3.22 +-Applying beta-rule and splitting (122), into two cases.
% 11.20/3.22 |-Branch one:
% 11.20/3.22 | (130) ~ (all_49_0_55 = 0) & subset(all_0_1_1, all_0_3_3) = all_49_0_55
% 11.20/3.22 |
% 11.20/3.22 | Applying alpha-rule on (130) yields:
% 11.20/3.22 | (131) ~ (all_49_0_55 = 0)
% 11.20/3.22 | (132) subset(all_0_1_1, all_0_3_3) = all_49_0_55
% 11.20/3.22 |
% 11.20/3.22 | Instantiating formula (58) with all_49_0_55, all_0_3_3, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_3_3) = all_49_0_55, yields:
% 11.20/3.22 | (133) all_49_0_55 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1)
% 11.20/3.22 |
% 11.20/3.22 +-Applying beta-rule and splitting (133), into two cases.
% 11.20/3.22 |-Branch one:
% 11.20/3.22 | (134) all_49_0_55 = 0
% 11.20/3.22 |
% 11.20/3.22 | Equations (134) can reduce 131 to:
% 11.20/3.22 | (119) $false
% 11.20/3.22 |
% 11.20/3.22 |-The branch is then unsatisfiable
% 11.20/3.22 |-Branch two:
% 11.20/3.22 | (131) ~ (all_49_0_55 = 0)
% 11.20/3.22 | (137) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_3_3) = v1)
% 11.20/3.22 |
% 11.20/3.22 | Instantiating (137) with all_95_0_89, all_95_1_90 yields:
% 11.20/3.22 | (138) ~ (all_95_0_89 = 0) & member(all_95_1_90, all_0_1_1) = 0 & member(all_95_1_90, all_0_3_3) = all_95_0_89
% 11.20/3.22 |
% 11.20/3.22 | Applying alpha-rule on (138) yields:
% 11.20/3.22 | (139) ~ (all_95_0_89 = 0)
% 11.20/3.22 | (140) member(all_95_1_90, all_0_1_1) = 0
% 11.20/3.22 | (141) member(all_95_1_90, all_0_3_3) = all_95_0_89
% 11.20/3.22 |
% 11.20/3.22 | Instantiating formula (39) with all_0_1_1, all_0_2_2, all_0_3_3, all_95_1_90 and discharging atoms intersection(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_95_1_90, all_0_1_1) = 0, yields:
% 11.20/3.22 | (142) member(all_95_1_90, all_0_2_2) = 0 & member(all_95_1_90, all_0_3_3) = 0
% 11.20/3.22 |
% 11.20/3.22 | Applying alpha-rule on (142) yields:
% 11.20/3.22 | (143) member(all_95_1_90, all_0_2_2) = 0
% 11.20/3.22 | (144) member(all_95_1_90, all_0_3_3) = 0
% 11.20/3.22 |
% 11.20/3.22 | Instantiating formula (42) with all_95_0_89, all_0_3_3, all_95_1_90 and discharging atoms member(all_95_1_90, all_0_3_3) = all_95_0_89, yields:
% 11.20/3.22 | (145) all_95_0_89 = 0 | ? [v0] : ( ~ (v0 = 0) & apply(member_predicate, all_95_1_90, all_0_3_3) = v0)
% 11.20/3.22 |
% 11.20/3.22 +-Applying beta-rule and splitting (145), into two cases.
% 11.20/3.22 |-Branch one:
% 11.20/3.22 | (146) all_95_0_89 = 0
% 11.20/3.22 |
% 11.20/3.22 | Equations (146) can reduce 139 to:
% 11.20/3.22 | (119) $false
% 11.20/3.22 |
% 11.20/3.22 |-The branch is then unsatisfiable
% 11.20/3.22 |-Branch two:
% 11.20/3.22 | (139) ~ (all_95_0_89 = 0)
% 11.20/3.22 | (149) ? [v0] : ( ~ (v0 = 0) & apply(member_predicate, all_95_1_90, all_0_3_3) = v0)
% 11.20/3.22 |
% 11.20/3.22 | Instantiating formula (60) with all_95_1_90, all_0_3_3, 0, all_95_0_89 and discharging atoms member(all_95_1_90, all_0_3_3) = all_95_0_89, member(all_95_1_90, all_0_3_3) = 0, yields:
% 11.20/3.22 | (146) all_95_0_89 = 0
% 11.20/3.22 |
% 11.20/3.22 | Equations (146) can reduce 139 to:
% 11.20/3.22 | (119) $false
% 11.20/3.22 |
% 11.20/3.22 |-The branch is then unsatisfiable
% 11.20/3.22 |-Branch two:
% 11.20/3.22 | (152) ~ (all_49_0_55 = 0) & subset(all_0_3_3, all_0_1_1) = all_49_0_55
% 11.20/3.22 |
% 11.20/3.22 | Applying alpha-rule on (152) yields:
% 11.20/3.22 | (131) ~ (all_49_0_55 = 0)
% 11.20/3.22 | (154) subset(all_0_3_3, all_0_1_1) = all_49_0_55
% 11.20/3.22 |
% 11.20/3.22 | Instantiating formula (5) with all_49_0_55, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_49_0_55, yields:
% 11.20/3.22 | (155) all_49_0_55 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_1_1) = v0 & member(all_0_3_3, v0) = v1)
% 11.20/3.22 |
% 11.20/3.22 | Instantiating formula (58) with all_49_0_55, all_0_1_1, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_1_1) = all_49_0_55, yields:
% 11.20/3.22 | (156) all_49_0_55 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 11.20/3.22 |
% 11.20/3.22 +-Applying beta-rule and splitting (155), into two cases.
% 11.20/3.22 |-Branch one:
% 11.20/3.22 | (134) all_49_0_55 = 0
% 11.20/3.22 |
% 11.20/3.22 | Equations (134) can reduce 131 to:
% 11.20/3.22 | (119) $false
% 11.20/3.22 |
% 11.20/3.22 |-The branch is then unsatisfiable
% 11.20/3.22 |-Branch two:
% 11.20/3.22 | (131) ~ (all_49_0_55 = 0)
% 11.20/3.22 | (160) ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_1_1) = v0 & member(all_0_3_3, v0) = v1)
% 11.20/3.22 |
% 11.20/3.22 +-Applying beta-rule and splitting (156), into two cases.
% 11.20/3.22 |-Branch one:
% 11.20/3.22 | (134) all_49_0_55 = 0
% 11.20/3.22 |
% 11.22/3.22 | Equations (134) can reduce 131 to:
% 11.22/3.22 | (119) $false
% 11.22/3.22 |
% 11.22/3.22 |-The branch is then unsatisfiable
% 11.22/3.22 |-Branch two:
% 11.22/3.22 | (131) ~ (all_49_0_55 = 0)
% 11.22/3.22 | (164) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_3_3) = 0)
% 11.22/3.22 |
% 11.22/3.22 | Instantiating (164) with all_99_0_128, all_99_1_129 yields:
% 11.22/3.22 | (165) ~ (all_99_0_128 = 0) & member(all_99_1_129, all_0_1_1) = all_99_0_128 & member(all_99_1_129, all_0_3_3) = 0
% 11.22/3.22 |
% 11.22/3.22 | Applying alpha-rule on (165) yields:
% 11.22/3.22 | (166) ~ (all_99_0_128 = 0)
% 11.22/3.22 | (167) member(all_99_1_129, all_0_1_1) = all_99_0_128
% 11.22/3.22 | (168) member(all_99_1_129, all_0_3_3) = 0
% 11.22/3.22 |
% 11.22/3.22 | Instantiating formula (80) with all_99_0_128, all_0_1_1, all_0_2_2, all_0_3_3, all_99_1_129 and discharging atoms intersection(all_0_3_3, all_0_2_2) = all_0_1_1, member(all_99_1_129, all_0_1_1) = all_99_0_128, yields:
% 11.22/3.22 | (169) all_99_0_128 = 0 | ? [v0] : (( ~ (v0 = 0) & member(all_99_1_129, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_99_1_129, all_0_3_3) = v0))
% 11.22/3.22 |
% 11.22/3.22 | Instantiating formula (42) with all_99_0_128, all_0_1_1, all_99_1_129 and discharging atoms member(all_99_1_129, all_0_1_1) = all_99_0_128, yields:
% 11.22/3.22 | (170) all_99_0_128 = 0 | ? [v0] : ( ~ (v0 = 0) & apply(member_predicate, all_99_1_129, all_0_1_1) = v0)
% 11.22/3.22 |
% 11.22/3.22 | Instantiating formula (129) with all_99_1_129 and discharging atoms member(all_99_1_129, all_0_3_3) = 0, yields:
% 11.22/3.22 | (171) subset(all_99_1_129, all_0_3_3) = 0
% 11.22/3.22 |
% 11.22/3.22 +-Applying beta-rule and splitting (170), into two cases.
% 11.22/3.22 |-Branch one:
% 11.22/3.22 | (172) all_99_0_128 = 0
% 11.22/3.22 |
% 11.22/3.22 | Equations (172) can reduce 166 to:
% 11.22/3.22 | (119) $false
% 11.22/3.22 |
% 11.22/3.22 |-The branch is then unsatisfiable
% 11.22/3.22 |-Branch two:
% 11.22/3.22 | (166) ~ (all_99_0_128 = 0)
% 11.22/3.22 | (175) ? [v0] : ( ~ (v0 = 0) & apply(member_predicate, all_99_1_129, all_0_1_1) = v0)
% 11.22/3.22 |
% 11.22/3.22 +-Applying beta-rule and splitting (169), into two cases.
% 11.22/3.22 |-Branch one:
% 11.22/3.22 | (172) all_99_0_128 = 0
% 11.22/3.22 |
% 11.22/3.22 | Equations (172) can reduce 166 to:
% 11.22/3.22 | (119) $false
% 11.22/3.22 |
% 11.22/3.22 |-The branch is then unsatisfiable
% 11.22/3.22 |-Branch two:
% 11.22/3.22 | (166) ~ (all_99_0_128 = 0)
% 11.22/3.22 | (179) ? [v0] : (( ~ (v0 = 0) & member(all_99_1_129, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_99_1_129, all_0_3_3) = v0))
% 11.22/3.22 |
% 11.22/3.22 | Instantiating (179) with all_119_0_134 yields:
% 11.22/3.22 | (180) ( ~ (all_119_0_134 = 0) & member(all_99_1_129, all_0_2_2) = all_119_0_134) | ( ~ (all_119_0_134 = 0) & member(all_99_1_129, all_0_3_3) = all_119_0_134)
% 11.22/3.22 |
% 11.22/3.22 +-Applying beta-rule and splitting (180), into two cases.
% 11.22/3.22 |-Branch one:
% 11.22/3.22 | (181) ~ (all_119_0_134 = 0) & member(all_99_1_129, all_0_2_2) = all_119_0_134
% 11.22/3.22 |
% 11.22/3.22 | Applying alpha-rule on (181) yields:
% 11.22/3.22 | (182) ~ (all_119_0_134 = 0)
% 11.22/3.22 | (183) member(all_99_1_129, all_0_2_2) = all_119_0_134
% 11.22/3.22 |
% 11.22/3.22 | Instantiating formula (45) with all_119_0_134, all_0_2_2, all_0_3_3, all_99_1_129 and discharging atoms power_set(all_0_3_3) = all_0_2_2, member(all_99_1_129, all_0_2_2) = all_119_0_134, yields:
% 11.22/3.22 | (184) all_119_0_134 = 0 | ? [v0] : ( ~ (v0 = 0) & subset(all_99_1_129, all_0_3_3) = v0)
% 11.22/3.22 |
% 11.22/3.22 +-Applying beta-rule and splitting (184), into two cases.
% 11.22/3.22 |-Branch one:
% 11.22/3.22 | (185) all_119_0_134 = 0
% 11.22/3.22 |
% 11.22/3.22 | Equations (185) can reduce 182 to:
% 11.22/3.22 | (119) $false
% 11.22/3.22 |
% 11.22/3.22 |-The branch is then unsatisfiable
% 11.22/3.22 |-Branch two:
% 11.22/3.22 | (182) ~ (all_119_0_134 = 0)
% 11.22/3.22 | (188) ? [v0] : ( ~ (v0 = 0) & subset(all_99_1_129, all_0_3_3) = v0)
% 11.22/3.22 |
% 11.22/3.22 | Instantiating (188) with all_154_0_150 yields:
% 11.22/3.22 | (189) ~ (all_154_0_150 = 0) & subset(all_99_1_129, all_0_3_3) = all_154_0_150
% 11.22/3.22 |
% 11.22/3.22 | Applying alpha-rule on (189) yields:
% 11.22/3.22 | (190) ~ (all_154_0_150 = 0)
% 11.22/3.22 | (191) subset(all_99_1_129, all_0_3_3) = all_154_0_150
% 11.22/3.22 |
% 11.22/3.22 | Instantiating formula (20) with all_99_1_129, all_0_3_3, all_154_0_150, 0 and discharging atoms subset(all_99_1_129, all_0_3_3) = all_154_0_150, subset(all_99_1_129, all_0_3_3) = 0, yields:
% 11.22/3.22 | (192) all_154_0_150 = 0
% 11.22/3.22 |
% 11.22/3.22 | Equations (192) can reduce 190 to:
% 11.22/3.22 | (119) $false
% 11.22/3.22 |
% 11.22/3.22 |-The branch is then unsatisfiable
% 11.22/3.22 |-Branch two:
% 11.22/3.22 | (194) ~ (all_119_0_134 = 0) & member(all_99_1_129, all_0_3_3) = all_119_0_134
% 11.22/3.22 |
% 11.22/3.22 | Applying alpha-rule on (194) yields:
% 11.22/3.22 | (182) ~ (all_119_0_134 = 0)
% 11.22/3.22 | (196) member(all_99_1_129, all_0_3_3) = all_119_0_134
% 11.22/3.22 |
% 11.22/3.22 | Instantiating formula (60) with all_99_1_129, all_0_3_3, all_119_0_134, 0 and discharging atoms member(all_99_1_129, all_0_3_3) = all_119_0_134, member(all_99_1_129, all_0_3_3) = 0, yields:
% 11.22/3.22 | (185) all_119_0_134 = 0
% 11.22/3.22 |
% 11.22/3.22 | Equations (185) can reduce 182 to:
% 11.22/3.22 | (119) $false
% 11.22/3.22 |
% 11.22/3.22 |-The branch is then unsatisfiable
% 11.22/3.22 |-Branch two:
% 11.22/3.22 | (199) ~ (all_57_0_57 = 0) & member(all_0_3_3, on) = all_57_0_57
% 11.22/3.22 |
% 11.22/3.22 | Applying alpha-rule on (199) yields:
% 11.22/3.22 | (200) ~ (all_57_0_57 = 0)
% 11.22/3.22 | (201) member(all_0_3_3, on) = all_57_0_57
% 11.22/3.22 |
% 11.22/3.22 | Instantiating formula (60) with all_0_3_3, on, all_57_0_57, 0 and discharging atoms member(all_0_3_3, on) = all_57_0_57, member(all_0_3_3, on) = 0, yields:
% 11.22/3.22 | (126) all_57_0_57 = 0
% 11.22/3.22 |
% 11.22/3.22 | Equations (126) can reduce 200 to:
% 11.22/3.22 | (119) $false
% 11.22/3.22 |
% 11.22/3.22 |-The branch is then unsatisfiable
% 11.22/3.22 % SZS output end Proof for theBenchmark
% 11.22/3.22
% 11.22/3.22 2602ms
%------------------------------------------------------------------------------