TSTP Solution File: SET811+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET811+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n016.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 00:22:13 EDT 2022
% Result : Theorem 7.27s 2.33s
% Output : Proof 10.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET811+4 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n016.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 : Sun Jul 10 13:54:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.60/0.59 ____ _
% 0.60/0.59 ___ / __ \_____(_)___ ________ __________
% 0.60/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.59
% 0.60/0.59 A Theorem Prover for First-Order Logic
% 0.60/0.59 (ePrincess v.1.0)
% 0.60/0.59
% 0.60/0.59 (c) Philipp Rümmer, 2009-2015
% 0.60/0.59 (c) Peter Backeman, 2014-2015
% 0.60/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.59 Bug reports to peter@backeman.se
% 0.60/0.59
% 0.60/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.59
% 0.60/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.71/0.97 Prover 0: Preprocessing ...
% 2.65/1.24 Prover 0: Warning: ignoring some quantifiers
% 2.65/1.27 Prover 0: Constructing countermodel ...
% 4.52/1.72 Prover 0: gave up
% 4.52/1.72 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.52/1.75 Prover 1: Preprocessing ...
% 4.99/1.89 Prover 1: Constructing countermodel ...
% 5.81/2.01 Prover 1: gave up
% 5.81/2.01 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.81/2.03 Prover 2: Preprocessing ...
% 6.39/2.17 Prover 2: Warning: ignoring some quantifiers
% 6.39/2.18 Prover 2: Constructing countermodel ...
% 7.27/2.33 Prover 2: proved (322ms)
% 7.27/2.33
% 7.27/2.33 No countermodel exists, formula is valid
% 7.27/2.33 % SZS status Theorem for theBenchmark
% 7.27/2.33
% 7.27/2.33 Generating proof ... Warning: ignoring some quantifiers
% 9.93/2.94 found it (size 58)
% 9.93/2.94
% 9.93/2.94 % SZS output start Proof for theBenchmark
% 9.93/2.94 Assumed formulas after preprocessing and simplification:
% 9.93/2.94 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = 0) & initial_segment(v1, member_predicate, v0) = v2 & equal_set(v1, v2) = v3 & member(v1, v0) = 0 & 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)
% 10.33/3.01 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 10.33/3.01 | (1) ~ (all_0_0_0 = 0) & initial_segment(all_0_2_2, member_predicate, all_0_3_3) = all_0_1_1 & equal_set(all_0_2_2, all_0_1_1) = all_0_0_0 & member(all_0_2_2, all_0_3_3) = 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
% 10.33/3.04 |
% 10.33/3.04 | Applying alpha-rule on (1) yields:
% 10.33/3.04 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 10.33/3.04 | (3) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 10.33/3.04 | (4) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 10.33/3.04 | (5) ! [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)))
% 10.33/3.04 | (6) ! [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)))
% 10.33/3.04 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 10.33/3.04 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 10.33/3.04 | (9) ~ (all_0_0_0 = 0)
% 10.33/3.04 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 10.33/3.04 | (11) ! [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))
% 10.33/3.04 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 10.33/3.04 | (13) ! [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)))
% 10.33/3.04 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 10.33/3.04 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 10.33/3.04 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 10.33/3.04 | (17) ! [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)))
% 10.33/3.05 | (18) ! [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)))
% 10.33/3.05 | (19) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 10.33/3.05 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 10.33/3.05 | (21) ! [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)))
% 10.33/3.05 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strict_order(v3, v2) = v1) | ~ (strict_order(v3, v2) = v0))
% 10.33/3.05 | (23) ? [v0] : ? [v1] : sum(v0) = v1
% 10.33/3.05 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 10.33/3.05 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 10.33/3.05 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 10.33/3.05 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strict_well_order(v3, v2) = v1) | ~ (strict_well_order(v3, v2) = v0))
% 10.33/3.05 | (28) ! [v0] : ! [v1] : ( ~ (set(v0) = 0) | ~ (member(v1, v0) = 0) | set(v1) = 0)
% 10.33/3.05 | (29) ! [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)))
% 10.33/3.05 | (30) ! [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)))
% 10.33/3.05 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strict_order(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & strict_well_order(v0, v1) = v3))
% 10.33/3.05 | (32) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3
% 10.33/3.05 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set(v2) = v1) | ~ (set(v2) = v0))
% 10.33/3.05 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 10.33/3.05 | (35) member(all_0_2_2, all_0_3_3) = 0
% 10.33/3.05 | (36) ? [v0] : ? [v1] : power_set(v0) = v1
% 10.33/3.05 | (37) ! [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)))
% 10.33/3.05 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 10.33/3.05 | (39) ? [v0] : ? [v1] : singleton(v0) = v1
% 10.33/3.05 | (40) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 10.33/3.05 | (41) ! [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)))
% 10.33/3.05 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 10.33/3.05 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 10.33/3.05 | (44) ! [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))
% 10.33/3.05 | (45) ! [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)))
% 10.33/3.06 | (46) ! [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)))
% 10.33/3.06 | (47) ! [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)))
% 10.33/3.06 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (suc(v0) = v2) | ~ (member(v1, v2) = 0) | ? [v3] : ? [v4] : (singleton(v0) = v3 & union(v0, v3) = v4 & member(v1, v4) = 0))
% 10.33/3.06 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 10.33/3.06 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strict_well_order(v0, v1) = 0) | ~ (subset(v2, v1) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : least(v4, v0, v2) = 0)
% 10.33/3.06 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 10.33/3.06 | (52) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 10.33/3.06 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (initial_segment(v4, v3, v2) = v1) | ~ (initial_segment(v4, v3, v2) = v0))
% 10.33/3.06 | (54) ! [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)))
% 10.33/3.06 | (55) ! [v0] : ! [v1] : ( ~ (member(v0, v1) = 0) | apply(member_predicate, v0, v1) = 0)
% 10.33/3.06 | (56) ! [v0] : ! [v1] : ( ~ (apply(member_predicate, v0, v1) = 0) | member(v0, v1) = 0)
% 10.33/3.06 | (57) ? [v0] : ? [v1] : product(v0) = v1
% 10.33/3.06 | (58) ! [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))
% 10.33/3.06 | (59) ? [v0] : ? [v1] : suc(v0) = v1
% 10.33/3.06 | (60) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (member(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & apply(member_predicate, v0, v1) = v3))
% 10.33/3.06 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apply(member_predicate, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & member(v0, v1) = v3))
% 10.33/3.06 | (62) ! [v0] : ~ (member(v0, empty_set) = 0)
% 10.33/3.06 | (63) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 10.33/3.06 | (64) ! [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))
% 10.33/3.06 | (65) ! [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)))
% 10.33/3.06 | (66) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 10.33/3.06 | (67) ! [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)))
% 10.33/3.06 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 10.33/3.06 | (69) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 10.33/3.06 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (initial_segment(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | (apply(v1, v3, v0) = 0 & member(v3, v2) = 0))
% 10.33/3.06 | (71) ? [v0] : ? [v1] : ? [v2] : ? [v3] : least(v2, v1, v0) = v3
% 10.33/3.06 | (72) ! [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))
% 10.33/3.06 | (73) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (set(v1) = v2) | ~ (set(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3))
% 10.33/3.06 | (74) ? [v0] : ? [v1] : set(v0) = v1
% 10.33/3.06 | (75) ! [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)))
% 10.33/3.07 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 10.33/3.07 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 10.33/3.07 | (78) ! [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)))
% 10.33/3.07 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 10.33/3.07 | (80) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v0) = v2) | ~ (member(v0, on) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3))
% 10.33/3.07 | (81) ! [v0] : ! [v1] : ( ~ (strict_well_order(v0, v1) = 0) | strict_order(v0, v1) = 0)
% 10.33/3.07 | (82) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 10.33/3.07 | (83) initial_segment(all_0_2_2, member_predicate, all_0_3_3) = all_0_1_1
% 10.33/3.07 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 10.33/3.07 | (85) ! [v0] : ! [v1] : ( ~ (member(v1, v0) = 0) | ~ (member(v0, on) = 0) | subset(v1, v0) = 0)
% 10.33/3.07 | (86) ! [v0] : ( ~ (member(v0, on) = 0) | (strict_well_order(member_predicate, v0) = 0 & set(v0) = 0))
% 10.33/3.07 | (87) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (suc(v2) = v1) | ~ (suc(v2) = v0))
% 10.33/3.07 | (88) ! [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))
% 10.33/3.07 | (89) ? [v0] : ? [v1] : ? [v2] : strict_order(v1, v0) = v2
% 10.33/3.07 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 10.33/3.07 | (91) ! [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)))
% 10.33/3.07 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 10.33/3.07 | (93) ? [v0] : ? [v1] : ? [v2] : strict_well_order(v1, v0) = v2
% 10.33/3.07 | (94) ! [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)))
% 10.33/3.07 | (95) member(all_0_3_3, on) = 0
% 10.33/3.07 | (96) ? [v0] : ? [v1] : ? [v2] : ? [v3] : initial_segment(v2, v1, v0) = v3
% 10.33/3.07 | (97) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 10.33/3.07 | (98) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 10.33/3.07 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 10.33/3.07 | (100) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 10.33/3.07 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (least(v2, v0, v1) = 0) | ~ (member(v3, v1) = 0) | apply(v0, v2, v3) = 0)
% 10.33/3.07 | (102) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 10.33/3.07 | (103) ! [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))
% 10.33/3.07 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0))
% 10.33/3.07 | (105) equal_set(all_0_2_2, all_0_1_1) = all_0_0_0
% 10.33/3.07 | (106) ! [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)))
% 10.33/3.08 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 10.33/3.08 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (singleton(v0) = v2) | ~ (union(v0, v2) = v3) | ~ (member(v1, v3) = 0) | ? [v4] : (suc(v0) = v4 & member(v1, v4) = 0))
% 10.33/3.08 | (109) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 10.33/3.08 | (110) ! [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)))
% 10.33/3.08 | (111) ! [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)))
% 10.33/3.08 | (112) ! [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))
% 10.33/3.08 | (113) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 10.33/3.08 |
% 10.33/3.08 | Instantiating formula (16) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms equal_set(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 10.33/3.08 | (114) all_0_0_0 = 0 | ? [v0] : (( ~ (v0 = 0) & subset(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & subset(all_0_2_2, all_0_1_1) = v0))
% 10.33/3.08 |
% 10.33/3.08 | Instantiating formula (85) with all_0_2_2, all_0_3_3 and discharging atoms member(all_0_2_2, all_0_3_3) = 0, member(all_0_3_3, on) = 0, yields:
% 10.33/3.08 | (115) subset(all_0_2_2, all_0_3_3) = 0
% 10.33/3.08 |
% 10.33/3.08 +-Applying beta-rule and splitting (114), into two cases.
% 10.33/3.08 |-Branch one:
% 10.33/3.08 | (116) all_0_0_0 = 0
% 10.33/3.08 |
% 10.33/3.08 | Equations (116) can reduce 9 to:
% 10.33/3.08 | (117) $false
% 10.33/3.08 |
% 10.73/3.08 |-The branch is then unsatisfiable
% 10.73/3.08 |-Branch two:
% 10.73/3.08 | (9) ~ (all_0_0_0 = 0)
% 10.73/3.08 | (119) ? [v0] : (( ~ (v0 = 0) & subset(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & subset(all_0_2_2, all_0_1_1) = v0))
% 10.73/3.08 |
% 10.73/3.08 | Instantiating (119) with all_49_0_55 yields:
% 10.73/3.08 | (120) ( ~ (all_49_0_55 = 0) & subset(all_0_1_1, all_0_2_2) = all_49_0_55) | ( ~ (all_49_0_55 = 0) & subset(all_0_2_2, all_0_1_1) = all_49_0_55)
% 10.73/3.08 |
% 10.73/3.08 +-Applying beta-rule and splitting (120), into two cases.
% 10.73/3.08 |-Branch one:
% 10.73/3.08 | (121) ~ (all_49_0_55 = 0) & subset(all_0_1_1, all_0_2_2) = all_49_0_55
% 10.73/3.08 |
% 10.73/3.08 | Applying alpha-rule on (121) yields:
% 10.73/3.08 | (122) ~ (all_49_0_55 = 0)
% 10.73/3.09 | (123) subset(all_0_1_1, all_0_2_2) = all_49_0_55
% 10.73/3.09 |
% 10.73/3.09 | Instantiating formula (113) with all_49_0_55, all_0_2_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_2_2) = all_49_0_55, yields:
% 10.73/3.09 | (124) all_49_0_55 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_2_2) = v0 & member(all_0_1_1, v0) = v1)
% 10.73/3.09 |
% 10.73/3.09 | Instantiating formula (102) with all_49_0_55, all_0_2_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_2_2) = all_49_0_55, yields:
% 10.73/3.09 | (125) all_49_0_55 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_2_2) = v1)
% 10.73/3.09 |
% 10.73/3.09 +-Applying beta-rule and splitting (124), into two cases.
% 10.73/3.09 |-Branch one:
% 10.73/3.09 | (126) all_49_0_55 = 0
% 10.73/3.09 |
% 10.73/3.09 | Equations (126) can reduce 122 to:
% 10.73/3.09 | (117) $false
% 10.73/3.09 |
% 10.73/3.09 |-The branch is then unsatisfiable
% 10.73/3.09 |-Branch two:
% 10.73/3.09 | (122) ~ (all_49_0_55 = 0)
% 10.73/3.09 | (129) ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_2_2) = v0 & member(all_0_1_1, v0) = v1)
% 10.73/3.09 |
% 10.73/3.09 +-Applying beta-rule and splitting (125), into two cases.
% 10.73/3.09 |-Branch one:
% 10.73/3.09 | (126) all_49_0_55 = 0
% 10.73/3.09 |
% 10.73/3.09 | Equations (126) can reduce 122 to:
% 10.73/3.09 | (117) $false
% 10.73/3.09 |
% 10.73/3.09 |-The branch is then unsatisfiable
% 10.73/3.09 |-Branch two:
% 10.73/3.09 | (122) ~ (all_49_0_55 = 0)
% 10.73/3.09 | (133) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_2_2) = v1)
% 10.73/3.09 |
% 10.73/3.09 | Instantiating (133) with all_131_0_108, all_131_1_109 yields:
% 10.73/3.09 | (134) ~ (all_131_0_108 = 0) & member(all_131_1_109, all_0_1_1) = 0 & member(all_131_1_109, all_0_2_2) = all_131_0_108
% 10.73/3.09 |
% 10.73/3.09 | Applying alpha-rule on (134) yields:
% 10.73/3.09 | (135) ~ (all_131_0_108 = 0)
% 10.73/3.09 | (136) member(all_131_1_109, all_0_1_1) = 0
% 10.73/3.09 | (137) member(all_131_1_109, all_0_2_2) = all_131_0_108
% 10.73/3.09 |
% 10.73/3.09 | Instantiating formula (70) with all_0_1_1, all_131_1_109, all_0_3_3, member_predicate, all_0_2_2 and discharging atoms initial_segment(all_0_2_2, member_predicate, all_0_3_3) = all_0_1_1, member(all_131_1_109, all_0_1_1) = 0, yields:
% 10.73/3.09 | (138) apply(member_predicate, all_131_1_109, all_0_2_2) = 0 & member(all_131_1_109, all_0_3_3) = 0
% 10.73/3.09 |
% 10.73/3.09 | Applying alpha-rule on (138) yields:
% 10.73/3.09 | (139) apply(member_predicate, all_131_1_109, all_0_2_2) = 0
% 10.73/3.09 | (140) member(all_131_1_109, all_0_3_3) = 0
% 10.73/3.09 |
% 10.73/3.09 | Instantiating formula (60) with all_131_0_108, all_0_2_2, all_131_1_109 and discharging atoms member(all_131_1_109, all_0_2_2) = all_131_0_108, yields:
% 10.73/3.09 | (141) all_131_0_108 = 0 | ? [v0] : ( ~ (v0 = 0) & apply(member_predicate, all_131_1_109, all_0_2_2) = v0)
% 10.73/3.09 |
% 10.73/3.09 +-Applying beta-rule and splitting (141), into two cases.
% 10.73/3.09 |-Branch one:
% 10.73/3.09 | (142) all_131_0_108 = 0
% 10.73/3.09 |
% 10.73/3.09 | Equations (142) can reduce 135 to:
% 10.73/3.09 | (117) $false
% 10.73/3.09 |
% 10.73/3.09 |-The branch is then unsatisfiable
% 10.73/3.09 |-Branch two:
% 10.73/3.09 | (135) ~ (all_131_0_108 = 0)
% 10.73/3.09 | (145) ? [v0] : ( ~ (v0 = 0) & apply(member_predicate, all_131_1_109, all_0_2_2) = v0)
% 10.73/3.09 |
% 10.73/3.09 | Instantiating (145) with all_151_0_110 yields:
% 10.73/3.09 | (146) ~ (all_151_0_110 = 0) & apply(member_predicate, all_131_1_109, all_0_2_2) = all_151_0_110
% 10.73/3.09 |
% 10.73/3.09 | Applying alpha-rule on (146) yields:
% 10.73/3.09 | (147) ~ (all_151_0_110 = 0)
% 10.73/3.09 | (148) apply(member_predicate, all_131_1_109, all_0_2_2) = all_151_0_110
% 10.73/3.09 |
% 10.73/3.09 | Instantiating formula (77) with member_predicate, all_131_1_109, all_0_2_2, 0, all_151_0_110 and discharging atoms apply(member_predicate, all_131_1_109, all_0_2_2) = all_151_0_110, apply(member_predicate, all_131_1_109, all_0_2_2) = 0, yields:
% 10.73/3.09 | (149) all_151_0_110 = 0
% 10.73/3.09 |
% 10.73/3.09 | Equations (149) can reduce 147 to:
% 10.73/3.09 | (117) $false
% 10.73/3.09 |
% 10.73/3.09 |-The branch is then unsatisfiable
% 10.73/3.09 |-Branch two:
% 10.73/3.09 | (151) ~ (all_49_0_55 = 0) & subset(all_0_2_2, all_0_1_1) = all_49_0_55
% 10.73/3.09 |
% 10.73/3.09 | Applying alpha-rule on (151) yields:
% 10.73/3.09 | (122) ~ (all_49_0_55 = 0)
% 10.73/3.09 | (153) subset(all_0_2_2, all_0_1_1) = all_49_0_55
% 10.73/3.09 |
% 10.73/3.09 | Instantiating formula (113) with all_49_0_55, all_0_1_1, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_1_1) = all_49_0_55, yields:
% 10.73/3.09 | (154) all_49_0_55 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_1_1) = v0 & member(all_0_2_2, v0) = v1)
% 10.73/3.09 |
% 10.73/3.09 | Instantiating formula (102) with all_49_0_55, all_0_1_1, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_1_1) = all_49_0_55, yields:
% 10.73/3.09 | (155) all_49_0_55 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0)
% 10.73/3.09 |
% 10.73/3.09 +-Applying beta-rule and splitting (154), into two cases.
% 10.73/3.09 |-Branch one:
% 10.73/3.09 | (126) all_49_0_55 = 0
% 10.73/3.09 |
% 10.73/3.09 | Equations (126) can reduce 122 to:
% 10.73/3.09 | (117) $false
% 10.73/3.09 |
% 10.73/3.09 |-The branch is then unsatisfiable
% 10.73/3.09 |-Branch two:
% 10.73/3.09 | (122) ~ (all_49_0_55 = 0)
% 10.73/3.09 | (159) ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_1_1) = v0 & member(all_0_2_2, v0) = v1)
% 10.73/3.09 |
% 10.73/3.09 +-Applying beta-rule and splitting (155), into two cases.
% 10.73/3.09 |-Branch one:
% 10.73/3.09 | (126) all_49_0_55 = 0
% 10.73/3.09 |
% 10.73/3.09 | Equations (126) can reduce 122 to:
% 10.73/3.09 | (117) $false
% 10.73/3.09 |
% 10.73/3.09 |-The branch is then unsatisfiable
% 10.73/3.09 |-Branch two:
% 10.73/3.09 | (122) ~ (all_49_0_55 = 0)
% 10.73/3.09 | (163) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = v1 & member(v0, all_0_2_2) = 0)
% 10.73/3.09 |
% 10.73/3.09 | Instantiating (163) with all_127_0_120, all_127_1_121 yields:
% 10.73/3.09 | (164) ~ (all_127_0_120 = 0) & member(all_127_1_121, all_0_1_1) = all_127_0_120 & member(all_127_1_121, all_0_2_2) = 0
% 10.73/3.09 |
% 10.73/3.09 | Applying alpha-rule on (164) yields:
% 10.73/3.09 | (165) ~ (all_127_0_120 = 0)
% 10.73/3.09 | (166) member(all_127_1_121, all_0_1_1) = all_127_0_120
% 10.73/3.09 | (167) member(all_127_1_121, all_0_2_2) = 0
% 10.73/3.09 |
% 10.73/3.09 | Instantiating formula (21) with all_127_0_120, all_0_1_1, all_127_1_121, all_0_3_3, member_predicate, all_0_2_2 and discharging atoms initial_segment(all_0_2_2, member_predicate, all_0_3_3) = all_0_1_1, member(all_127_1_121, all_0_1_1) = all_127_0_120, yields:
% 10.73/3.09 | (168) all_127_0_120 = 0 | ? [v0] : (( ~ (v0 = 0) & apply(member_predicate, all_127_1_121, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_127_1_121, all_0_3_3) = v0))
% 10.73/3.10 |
% 10.73/3.10 | Instantiating formula (43) with all_127_1_121, all_0_3_3, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_3_3) = 0, member(all_127_1_121, all_0_2_2) = 0, yields:
% 10.73/3.10 | (169) member(all_127_1_121, all_0_3_3) = 0
% 10.73/3.10 |
% 10.73/3.10 | Instantiating formula (55) with all_0_2_2, all_127_1_121 and discharging atoms member(all_127_1_121, all_0_2_2) = 0, yields:
% 10.73/3.10 | (170) apply(member_predicate, all_127_1_121, all_0_2_2) = 0
% 10.73/3.10 |
% 10.73/3.10 +-Applying beta-rule and splitting (168), into two cases.
% 10.73/3.10 |-Branch one:
% 10.73/3.10 | (171) all_127_0_120 = 0
% 10.73/3.10 |
% 10.73/3.10 | Equations (171) can reduce 165 to:
% 10.73/3.10 | (117) $false
% 10.73/3.10 |
% 10.73/3.10 |-The branch is then unsatisfiable
% 10.73/3.10 |-Branch two:
% 10.73/3.10 | (165) ~ (all_127_0_120 = 0)
% 10.73/3.10 | (174) ? [v0] : (( ~ (v0 = 0) & apply(member_predicate, all_127_1_121, all_0_2_2) = v0) | ( ~ (v0 = 0) & member(all_127_1_121, all_0_3_3) = v0))
% 10.73/3.10 |
% 10.73/3.10 | Instantiating (174) with all_152_0_126 yields:
% 10.73/3.10 | (175) ( ~ (all_152_0_126 = 0) & apply(member_predicate, all_127_1_121, all_0_2_2) = all_152_0_126) | ( ~ (all_152_0_126 = 0) & member(all_127_1_121, all_0_3_3) = all_152_0_126)
% 10.73/3.10 |
% 10.73/3.10 +-Applying beta-rule and splitting (175), into two cases.
% 10.73/3.10 |-Branch one:
% 10.73/3.10 | (176) ~ (all_152_0_126 = 0) & apply(member_predicate, all_127_1_121, all_0_2_2) = all_152_0_126
% 10.73/3.10 |
% 10.73/3.10 | Applying alpha-rule on (176) yields:
% 10.73/3.10 | (177) ~ (all_152_0_126 = 0)
% 10.73/3.10 | (178) apply(member_predicate, all_127_1_121, all_0_2_2) = all_152_0_126
% 10.73/3.10 |
% 10.73/3.10 | Instantiating formula (77) with member_predicate, all_127_1_121, all_0_2_2, 0, all_152_0_126 and discharging atoms apply(member_predicate, all_127_1_121, all_0_2_2) = all_152_0_126, apply(member_predicate, all_127_1_121, all_0_2_2) = 0, yields:
% 10.73/3.10 | (179) all_152_0_126 = 0
% 10.73/3.10 |
% 10.73/3.10 | Equations (179) can reduce 177 to:
% 10.73/3.10 | (117) $false
% 10.73/3.10 |
% 10.73/3.10 |-The branch is then unsatisfiable
% 10.73/3.10 |-Branch two:
% 10.73/3.10 | (181) ~ (all_152_0_126 = 0) & member(all_127_1_121, all_0_3_3) = all_152_0_126
% 10.73/3.10 |
% 10.73/3.10 | Applying alpha-rule on (181) yields:
% 10.73/3.10 | (177) ~ (all_152_0_126 = 0)
% 10.73/3.10 | (183) member(all_127_1_121, all_0_3_3) = all_152_0_126
% 10.73/3.10 |
% 10.73/3.10 | Instantiating formula (34) with all_127_1_121, all_0_3_3, 0, all_152_0_126 and discharging atoms member(all_127_1_121, all_0_3_3) = all_152_0_126, member(all_127_1_121, all_0_3_3) = 0, yields:
% 10.73/3.10 | (179) all_152_0_126 = 0
% 10.73/3.10 |
% 10.73/3.10 | Equations (179) can reduce 177 to:
% 10.73/3.10 | (117) $false
% 10.73/3.10 |
% 10.73/3.10 |-The branch is then unsatisfiable
% 10.73/3.10 % SZS output end Proof for theBenchmark
% 10.73/3.10
% 10.73/3.10 2493ms
%------------------------------------------------------------------------------