TSTP Solution File: SET814+4 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET814+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n010.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 6.71s 2.16s
% Output : Proof 9.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET814+4 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n010.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 10 14:17:30 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.51/0.58 ____ _
% 0.51/0.58 ___ / __ \_____(_)___ ________ __________
% 0.51/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.58
% 0.51/0.58 A Theorem Prover for First-Order Logic
% 0.51/0.58 (ePrincess v.1.0)
% 0.51/0.58
% 0.51/0.58 (c) Philipp Rümmer, 2009-2015
% 0.51/0.58 (c) Peter Backeman, 2014-2015
% 0.51/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.58 Bug reports to peter@backeman.se
% 0.51/0.58
% 0.51/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.58
% 0.51/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.51/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.76/0.95 Prover 0: Preprocessing ...
% 2.48/1.21 Prover 0: Warning: ignoring some quantifiers
% 2.76/1.24 Prover 0: Constructing countermodel ...
% 4.06/1.55 Prover 0: gave up
% 4.06/1.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.20/1.59 Prover 1: Preprocessing ...
% 5.00/1.74 Prover 1: Constructing countermodel ...
% 5.33/1.82 Prover 1: gave up
% 5.33/1.82 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.33/1.85 Prover 2: Preprocessing ...
% 6.11/1.99 Prover 2: Warning: ignoring some quantifiers
% 6.11/1.99 Prover 2: Constructing countermodel ...
% 6.71/2.16 Prover 2: proved (333ms)
% 6.71/2.16
% 6.71/2.16 No countermodel exists, formula is valid
% 6.71/2.16 % SZS status Theorem for theBenchmark
% 6.71/2.16
% 6.71/2.16 Generating proof ... Warning: ignoring some quantifiers
% 9.02/2.66 found it (size 42)
% 9.02/2.66
% 9.02/2.66 % SZS output start Proof for theBenchmark
% 9.02/2.66 Assumed formulas after preprocessing and simplification:
% 9.02/2.66 | (0) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = 0) & sum(v0) = v1 & subset(v1, v0) = v2 & member(v0, on) = 0 & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (initial_segment(v3, v4, v5) = v7) | ~ (member(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apply(v4, v6, v3) = v9) | ( ~ (v9 = 0) & member(v6, v5) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apply(v3, v6, v7) = 0) | ~ (apply(v3, v5, v7) = v8) | ~ (strict_order(v3, v4) = 0) | ? [v9] : (( ~ (v9 = 0) & apply(v3, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v4) = v9) | ( ~ (v9 = 0) & member(v6, v4) = v9) | ( ~ (v9 = 0) & member(v5, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apply(v3, v5, v7) = v8) | ~ (apply(v3, v5, v6) = 0) | ~ (strict_order(v3, v4) = 0) | ? [v9] : (( ~ (v9 = 0) & apply(v3, v6, v7) = v9) | ( ~ (v9 = 0) & member(v7, v4) = v9) | ( ~ (v9 = 0) & member(v6, v4) = v9) | ( ~ (v9 = 0) & member(v5, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apply(v3, v5, v7) = v8) | ~ (strict_order(v3, v4) = 0) | ~ (member(v6, v4) = 0) | ? [v9] : (( ~ (v9 = 0) & apply(v3, v6, v7) = v9) | ( ~ (v9 = 0) & apply(v3, v5, v6) = v9) | ( ~ (v9 = 0) & member(v7, v4) = v9) | ( ~ (v9 = 0) & member(v5, v4) = v9))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v6 = v5 | ~ (apply(v3, v5, v6) = v7) | ~ (least(v5, v3, v4) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v6, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (product(v4) = v5) | ~ (member(v3, v6) = v7) | ~ (member(v3, v5) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v6, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (singleton(v3) = v5) | ~ (union(v3, v5) = v6) | ~ (member(v4, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & suc(v3) = v8 & member(v4, v8) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (difference(v5, v4) = v6) | ~ (member(v3, v6) = v7) | ? [v8] : ((v8 = 0 & member(v3, v4) = 0) | ( ~ (v8 = 0) & member(v3, v5) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (union(v4, v5) = v6) | ~ (member(v3, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v8 = 0) & member(v3, v5) = v9 & member(v3, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (intersection(v4, v5) = v6) | ~ (member(v3, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & member(v3, v5) = v8) | ( ~ (v8 = 0) & member(v3, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (sum(v4) = v5) | ~ (member(v7, v4) = 0) | ~ (member(v3, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & member(v3, v7) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (sum(v4) = v5) | ~ (member(v3, v7) = 0) | ~ (member(v3, v5) = v6) | ? [v8] : ( ~ (v8 = 0) & member(v7, v4) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v4 = v3 | ~ (initial_segment(v7, v6, v5) = v4) | ~ (initial_segment(v7, v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v4 = v3 | ~ (apply(v7, v6, v5) = v4) | ~ (apply(v7, v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v4 = v3 | ~ (least(v7, v6, v5) = v4) | ~ (least(v7, v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (initial_segment(v3, v4, v5) = v7) | ~ (member(v6, v7) = 0) | (apply(v4, v6, v3) = 0 & member(v6, v5) = 0)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v3, v6, v7) = 0) | ~ (apply(v3, v5, v6) = 0) | ~ (strict_order(v3, v4) = 0) | ? [v8] : ((v8 = 0 & apply(v3, v5, v7) = 0) | ( ~ (v8 = 0) & member(v7, v4) = v8) | ( ~ (v8 = 0) & member(v6, v4) = v8) | ( ~ (v8 = 0) & member(v5, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v3, v6, v7) = 0) | ~ (strict_order(v3, v4) = 0) | ~ (member(v5, v4) = 0) | ? [v8] : ((v8 = 0 & apply(v3, v5, v7) = 0) | ( ~ (v8 = 0) & apply(v3, v5, v6) = v8) | ( ~ (v8 = 0) & member(v7, v4) = v8) | ( ~ (v8 = 0) & member(v6, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (apply(v3, v5, v6) = 0) | ~ (strict_order(v3, v4) = 0) | ~ (member(v7, v4) = 0) | ? [v8] : ((v8 = 0 & apply(v3, v5, v7) = 0) | ( ~ (v8 = 0) & apply(v3, v6, v7) = v8) | ( ~ (v8 = 0) & member(v6, v4) = v8) | ( ~ (v8 = 0) & member(v5, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (strict_order(v3, v4) = v5) | ~ (subset(v6, v4) = 0) | ~ (member(v7, v6) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & least(v8, v3, v6) = 0) | ( ~ (v8 = 0) & strict_well_order(v3, v4) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (strict_order(v3, v4) = 0) | ~ (member(v7, v4) = 0) | ~ (member(v6, v4) = 0) | ~ (member(v5, v4) = 0) | ? [v8] : ((v8 = 0 & apply(v3, v5, v7) = 0) | ( ~ (v8 = 0) & apply(v3, v6, v7) = v8) | ( ~ (v8 = 0) & apply(v3, v5, v6) = v8))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v5 | ~ (least(v5, v3, v4) = 0) | ~ (member(v6, v4) = 0) | apply(v3, v5, v6) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (suc(v3) = v5) | ~ (member(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & singleton(v3) = v7 & union(v3, v7) = v8 & member(v4, v8) = v9)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (least(v5, v3, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ((v8 = 0 & ~ (v9 = 0) & ~ (v7 = v5) & apply(v3, v5, v7) = v9 & member(v7, v4) = 0) | ( ~ (v7 = 0) & member(v5, v4) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (product(v4) = v5) | ~ (member(v3, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & member(v7, v4) = 0 & member(v3, v7) = v8)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unordered_pair(v4, v3) = v5) | ~ (member(v3, v5) = v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unordered_pair(v3, v4) = v5) | ~ (member(v3, v5) = v6)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (power_set(v4) = v5) | ~ (member(v3, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & subset(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v4, v5) = 0) | ~ (subset(v3, v5) = v6) | ? [v7] : ( ~ (v7 = 0) & subset(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v3, v5) = v6) | ~ (subset(v3, v4) = 0) | ? [v7] : ( ~ (v7 = 0) & subset(v4, v5) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (subset(v3, v4) = 0) | ~ (member(v5, v4) = v6) | ? [v7] : ( ~ (v7 = 0) & member(v5, v3) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v5 = v3 | v4 = v3 | ~ (unordered_pair(v4, v5) = v6) | ~ (member(v3, v6) = 0)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (strict_order(v6, v5) = v4) | ~ (strict_order(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (strict_well_order(v6, v5) = v4) | ~ (strict_well_order(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (unordered_pair(v6, v5) = v4) | ~ (unordered_pair(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (difference(v6, v5) = v4) | ~ (difference(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (union(v6, v5) = v4) | ~ (union(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (intersection(v6, v5) = v4) | ~ (intersection(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (equal_set(v6, v5) = v4) | ~ (equal_set(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (subset(v6, v5) = v4) | ~ (subset(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = v3 | ~ (member(v6, v5) = v4) | ~ (member(v6, v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (apply(v3, v6, v5) = 0) | ~ (strict_order(v3, v4) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v3, v5, v6) = v7) | ( ~ (v7 = 0) & member(v6, v4) = v7) | ( ~ (v7 = 0) & member(v5, v4) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (apply(v3, v5, v6) = 0) | ~ (strict_order(v3, v4) = 0) | ? [v7] : (( ~ (v7 = 0) & apply(v3, v6, v5) = v7) | ( ~ (v7 = 0) & member(v6, v4) = v7) | ( ~ (v7 = 0) & member(v5, v4) = v7))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (strict_well_order(v3, v4) = 0) | ~ (subset(v5, v4) = 0) | ~ (member(v6, v5) = 0) | ? [v7] : least(v7, v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (product(v4) = v5) | ~ (member(v6, v4) = 0) | ~ (member(v3, v5) = 0) | member(v3, v6) = 0) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (singleton(v3) = v5) | ~ (union(v3, v5) = v6) | ~ (member(v4, v6) = 0) | ? [v7] : (suc(v3) = v7 & member(v4, v7) = 0)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (difference(v5, v4) = v6) | ~ (member(v3, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & member(v3, v5) = 0 & member(v3, v4) = v7)) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (union(v4, v5) = v6) | ~ (member(v3, v6) = 0) | ? [v7] : ((v7 = 0 & member(v3, v5) = 0) | (v7 = 0 & member(v3, v4) = 0))) & ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection(v4, v5) = v6) | ~ (member(v3, v6) = 0) | (member(v3, v5) = 0 & member(v3, v4) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (apply(member_predicate, v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & member(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (strict_order(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v13 = 0 & v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & ~ (v14 = 0) & apply(v3, v7, v8) = 0 & apply(v3, v6, v8) = v14 & apply(v3, v6, v7) = 0 & member(v8, v4) = 0 & member(v7, v4) = 0 & member(v6, v4) = 0) | (v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & apply(v3, v7, v6) = 0 & apply(v3, v6, v7) = 0 & member(v7, v4) = 0 & member(v6, v4) = 0))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (strict_order(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & strict_well_order(v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (strict_well_order(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & v7 = 0 & subset(v6, v4) = 0 & member(v8, v6) = 0 & ! [v10] : ~ (least(v10, v3, v6) = 0)) | ( ~ (v6 = 0) & strict_order(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set(v4) = v5) | ~ (set(v3) = 0) | ? [v6] : ( ~ (v6 = 0) & member(v4, v3) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (singleton(v3) = v4) | ~ (member(v3, v4) = v5)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (equal_set(v3, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & subset(v4, v3) = v6) | ( ~ (v6 = 0) & subset(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v4, v3) = v5) | ~ (member(v3, on) = 0) | ? [v6] : ( ~ (v6 = 0) & member(v4, v3) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & power_set(v4) = v6 & member(v3, v6) = v7)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ( ~ (v7 = 0) & member(v6, v4) = v7 & member(v6, v3) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (member(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & apply(member_predicate, v3, v4) = v6)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (suc(v5) = v4) | ~ (suc(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (set(v5) = v4) | ~ (set(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (product(v5) = v4) | ~ (product(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (sum(v5) = v4) | ~ (sum(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (singleton(v5) = v4) | ~ (singleton(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (singleton(v4) = v5) | ~ (member(v3, v5) = 0)) & ! [v3] : ! [v4] : ! [v5] : (v4 = v3 | ~ (power_set(v5) = v4) | ~ (power_set(v5) = v3)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (suc(v3) = v5) | ~ (member(v4, v5) = 0) | ? [v6] : ? [v7] : (singleton(v3) = v6 & union(v3, v6) = v7 & member(v4, v7) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (least(v5, v3, v4) = 0) | member(v5, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (sum(v4) = v5) | ~ (member(v3, v5) = 0) | ? [v6] : (member(v6, v4) = 0 & member(v3, v6) = 0)) & ! [v3] : ! [v4] : ! [v5] : ( ~ (power_set(v4) = v5) | ~ (member(v3, v5) = 0) | subset(v3, v4) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (subset(v4, v5) = 0) | ~ (subset(v3, v4) = 0) | subset(v3, v5) = 0) & ! [v3] : ! [v4] : ! [v5] : ( ~ (subset(v4, v3) = v5) | ? [v6] : ((v6 = 0 & v5 = 0 & subset(v3, v4) = 0) | ( ~ (v6 = 0) & equal_set(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (subset(v3, v4) = v5) | ? [v6] : ((v6 = 0 & v5 = 0 & subset(v4, v3) = 0) | ( ~ (v6 = 0) & equal_set(v3, v4) = v6))) & ! [v3] : ! [v4] : ! [v5] : ( ~ (subset(v3, v4) = 0) | ~ (member(v5, v3) = 0) | member(v5, v4) = 0) & ! [v3] : ! [v4] : (v4 = 0 | ~ (member(v3, on) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & ~ (v7 = 0) & subset(v5, v3) = v7 & member(v5, v3) = 0) | ( ~ (v5 = 0) & strict_well_order(member_predicate, v3) = v5) | ( ~ (v5 = 0) & set(v3) = v5))) & ! [v3] : ! [v4] : ( ~ (apply(member_predicate, v3, v4) = 0) | member(v3, v4) = 0) & ! [v3] : ! [v4] : ( ~ (strict_order(v3, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ((v8 = 0 & v6 = 0 & subset(v5, v4) = 0 & member(v7, v5) = 0 & ! [v9] : ~ (least(v9, v3, v5) = 0)) | (v5 = 0 & strict_well_order(v3, v4) = 0))) & ! [v3] : ! [v4] : ( ~ (strict_well_order(v3, v4) = 0) | strict_order(v3, v4) = 0) & ! [v3] : ! [v4] : ( ~ (strict_well_order(member_predicate, v3) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & set(v3) = 0 & ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v6, v3) = v7) | ? [v8] : ( ~ (v8 = 0) & member(v6, v3) = v8)) & ! [v6] : ( ~ (member(v6, v3) = 0) | subset(v6, v3) = 0)) | ( ~ (v5 = 0) & member(v3, on) = v5))) & ! [v3] : ! [v4] : ( ~ (set(v3) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & strict_well_order(member_predicate, v3) = 0 & ! [v6] : ! [v7] : (v7 = 0 | ~ (subset(v6, v3) = v7) | ? [v8] : ( ~ (v8 = 0) & member(v6, v3) = v8)) & ! [v6] : ( ~ (member(v6, v3) = 0) | subset(v6, v3) = 0)) | ( ~ (v5 = 0) & member(v3, on) = v5))) & ! [v3] : ! [v4] : ( ~ (set(v3) = 0) | ~ (member(v4, v3) = 0) | set(v4) = 0) & ! [v3] : ! [v4] : ( ~ (equal_set(v3, v4) = 0) | (subset(v4, v3) = 0 & subset(v3, v4) = 0)) & ! [v3] : ! [v4] : ( ~ (subset(v4, v3) = 0) | ? [v5] : ((v5 = 0 & equal_set(v3, v4) = 0) | ( ~ (v5 = 0) & subset(v3, v4) = v5))) & ! [v3] : ! [v4] : ( ~ (subset(v3, v4) = 0) | ? [v5] : (power_set(v4) = v5 & member(v3, v5) = 0)) & ! [v3] : ! [v4] : ( ~ (subset(v3, v4) = 0) | ? [v5] : ((v5 = 0 & equal_set(v3, v4) = 0) | ( ~ (v5 = 0) & subset(v4, v3) = v5))) & ! [v3] : ! [v4] : ( ~ (member(v4, v3) = 0) | ~ (member(v3, on) = 0) | subset(v4, v3) = 0) & ! [v3] : ! [v4] : ( ~ (member(v3, v4) = 0) | apply(member_predicate, v3, v4) = 0) & ! [v3] : ( ~ (strict_well_order(member_predicate, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & subset(v4, v3) = v6 & member(v4, v3) = 0) | (v4 = 0 & member(v3, on) = 0) | ( ~ (v4 = 0) & set(v3) = v4))) & ! [v3] : ( ~ (set(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v5 = 0 & ~ (v6 = 0) & subset(v4, v3) = v6 & member(v4, v3) = 0) | (v4 = 0 & member(v3, on) = 0) | ( ~ (v4 = 0) & strict_well_order(member_predicate, v3) = v4))) & ! [v3] : ( ~ (member(v3, on) = 0) | (strict_well_order(member_predicate, v3) = 0 & set(v3) = 0)) & ! [v3] : ~ (member(v3, empty_set) = 0) & ? [v3] : ? [v4] : ? [v5] : ? [v6] : initial_segment(v5, v4, v3) = v6 & ? [v3] : ? [v4] : ? [v5] : ? [v6] : apply(v5, v4, v3) = v6 & ? [v3] : ? [v4] : ? [v5] : ? [v6] : least(v5, v4, v3) = v6 & ? [v3] : ? [v4] : ? [v5] : strict_order(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : strict_well_order(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : unordered_pair(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : difference(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : union(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : intersection(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : equal_set(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : subset(v4, v3) = v5 & ? [v3] : ? [v4] : ? [v5] : member(v4, v3) = v5 & ? [v3] : ? [v4] : suc(v3) = v4 & ? [v3] : ? [v4] : set(v3) = v4 & ? [v3] : ? [v4] : product(v3) = v4 & ? [v3] : ? [v4] : sum(v3) = v4 & ? [v3] : ? [v4] : singleton(v3) = v4 & ? [v3] : ? [v4] : power_set(v3) = v4)
% 9.02/2.71 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 9.02/2.71 | (1) ~ (all_0_0_0 = 0) & sum(all_0_2_2) = all_0_1_1 & subset(all_0_1_1, all_0_2_2) = all_0_0_0 & member(all_0_2_2, 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(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (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, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 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
% 9.02/2.74 |
% 9.02/2.74 | Applying alpha-rule on (1) yields:
% 9.02/2.74 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (suc(v2) = v1) | ~ (suc(v2) = v0))
% 9.50/2.74 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 9.50/2.74 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0))
% 9.50/2.74 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (initial_segment(v4, v3, v2) = v1) | ~ (initial_segment(v4, v3, v2) = v0))
% 9.50/2.74 | (6) ? [v0] : ? [v1] : ? [v2] : ? [v3] : apply(v2, v1, v0) = v3
% 9.50/2.74 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0)
% 9.50/2.74 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v1, v0) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 9.50/2.74 | (9) ! [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)))
% 9.50/2.74 | (10) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0))
% 9.50/2.74 | (11) ? [v0] : ? [v1] : ? [v2] : ? [v3] : least(v2, v1, v0) = v3
% 9.50/2.74 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strict_order(v3, v2) = v1) | ~ (strict_order(v3, v2) = v0))
% 9.50/2.74 | (13) ! [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)))
% 9.50/2.74 | (14) ! [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))
% 9.50/2.74 | (15) ! [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)))
% 9.50/2.74 | (16) ! [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)))
% 9.50/2.74 | (17) ? [v0] : ? [v1] : power_set(v0) = v1
% 9.50/2.74 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 9.50/2.74 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (member(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & apply(member_predicate, v0, v1) = v3))
% 9.50/2.74 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apply(member_predicate, v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & member(v0, v1) = v3))
% 9.50/2.74 | (21) ? [v0] : ? [v1] : ? [v2] : ? [v3] : initial_segment(v2, v1, v0) = v3
% 9.50/2.74 | (22) ! [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)))
% 9.50/2.74 | (23) ? [v0] : ? [v1] : suc(v0) = v1
% 9.50/2.74 | (24) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0))
% 9.50/2.74 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 9.50/2.74 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (strict_order(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & strict_well_order(v0, v1) = v3))
% 9.50/2.74 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 9.50/2.74 | (28) ? [v0] : ? [v1] : ? [v2] : strict_order(v1, v0) = v2
% 9.50/2.74 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & power_set(v1) = v3 & member(v0, v3) = v4))
% 9.50/2.74 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 9.50/2.74 | (31) ! [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))
% 9.50/2.74 | (32) ! [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)))
% 9.50/2.74 | (33) ! [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))
% 9.50/2.74 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0))
% 9.50/2.74 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 9.50/2.74 | (36) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 9.50/2.74 | (37) ! [v0] : ! [v1] : ( ~ (subset(v1, v0) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v0, v1) = v2)))
% 9.50/2.74 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_set(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & subset(v1, v0) = v3) | ( ~ (v3 = 0) & subset(v0, v1) = v3)))
% 9.50/2.75 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3))
% 9.50/2.75 | (40) ? [v0] : ? [v1] : ? [v2] : subset(v1, v0) = v2
% 9.50/2.75 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 9.50/2.75 | (42) ? [v0] : ? [v1] : set(v0) = v1
% 9.50/2.75 | (43) ! [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))
% 9.50/2.75 | (44) ! [v0] : ! [v1] : ( ~ (member(v1, v0) = 0) | ~ (member(v0, on) = 0) | subset(v1, v0) = 0)
% 9.50/2.75 | (45) ! [v0] : ! [v1] : ( ~ (set(v0) = 0) | ~ (member(v1, v0) = 0) | set(v1) = 0)
% 9.50/2.75 | (46) ? [v0] : ? [v1] : ? [v2] : difference(v1, v0) = v2
% 9.50/2.75 | (47) ! [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)))
% 9.50/2.75 | (48) ! [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))
% 9.50/2.75 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 9.50/2.75 | (50) ! [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)))
% 9.50/2.75 | (51) ! [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)))
% 9.50/2.75 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set(v2) = v1) | ~ (set(v2) = v0))
% 9.50/2.75 | (53) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 9.50/2.75 | (54) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (set(v1) = v2) | ~ (set(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3))
% 9.50/2.75 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 9.50/2.75 | (56) ! [v0] : ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 9.50/2.75 | (57) ! [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)))
% 9.50/2.75 | (58) ! [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))
% 9.50/2.75 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_set(v1) = v2) | ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 9.50/2.75 | (60) ! [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)))
% 9.50/2.75 | (61) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 9.50/2.75 | (62) ! [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)))
% 9.50/2.75 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 9.50/2.75 | (64) ! [v0] : ~ (member(v0, empty_set) = 0)
% 9.50/2.75 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (suc(v0) = v2) | ~ (member(v1, v2) = 0) | ? [v3] : ? [v4] : (singleton(v0) = v3 & union(v0, v3) = v4 & member(v1, v4) = 0))
% 9.50/2.75 | (66) ! [v0] : ! [v1] : ( ~ (strict_well_order(v0, v1) = 0) | strict_order(v0, v1) = 0)
% 9.50/2.75 | (67) ! [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)))
% 9.50/2.75 | (68) ? [v0] : ? [v1] : ? [v2] : strict_well_order(v1, v0) = v2
% 9.50/2.75 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 9.50/2.75 | (70) ! [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)))
% 9.50/2.75 | (71) ! [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)))
% 9.50/2.75 | (72) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (member(v0, v1) = v2))
% 9.50/2.75 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0))
% 9.50/2.75 | (74) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, v0) = v2) | ~ (member(v0, on) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3))
% 9.50/2.75 | (75) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0))
% 9.50/2.75 | (76) ! [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)))
% 9.50/2.76 | (77) ! [v0] : ( ~ (member(v0, on) = 0) | (strict_well_order(member_predicate, v0) = 0 & set(v0) = 0))
% 9.50/2.76 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (product(v1) = v2) | ~ (member(v3, v1) = 0) | ~ (member(v0, v2) = 0) | member(v0, v3) = 0)
% 9.50/2.76 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v1, v0) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & subset(v0, v1) = 0) | ( ~ (v3 = 0) & equal_set(v0, v1) = v3)))
% 9.50/2.76 | (80) ! [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)))
% 9.50/2.76 | (81) ! [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)))
% 9.50/2.76 | (82) ! [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)))
% 9.50/2.76 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 9.50/2.76 | (84) ! [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)))
% 9.50/2.76 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strict_well_order(v0, v1) = 0) | ~ (subset(v2, v1) = 0) | ~ (member(v3, v2) = 0) | ? [v4] : least(v4, v0, v2) = 0)
% 9.50/2.76 | (86) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : ((v2 = 0 & equal_set(v0, v1) = 0) | ( ~ (v2 = 0) & subset(v1, v0) = v2)))
% 9.50/2.76 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (least(v2, v0, v1) = 0) | member(v2, v1) = 0)
% 9.50/2.76 | (88) ~ (all_0_0_0 = 0)
% 9.50/2.76 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (least(v2, v0, v1) = 0) | ~ (member(v3, v1) = 0) | apply(v0, v2, v3) = 0)
% 9.50/2.76 | (90) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 9.50/2.76 | (91) ? [v0] : ? [v1] : ? [v2] : equal_set(v1, v0) = v2
% 9.50/2.76 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 9.50/2.76 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_set(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 9.50/2.76 | (94) ! [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)))
% 9.50/2.76 | (95) ! [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))
% 9.50/2.76 | (96) ! [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)))
% 9.50/2.76 | (97) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 9.50/2.76 | (98) ! [v0] : ! [v1] : ( ~ (subset(v0, v1) = 0) | ? [v2] : (power_set(v1) = v2 & member(v0, v2) = 0))
% 9.50/2.76 | (99) sum(all_0_2_2) = all_0_1_1
% 9.50/2.76 | (100) ? [v0] : ? [v1] : sum(v0) = v1
% 9.50/2.76 | (101) ! [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))
% 9.50/2.76 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0))
% 9.50/2.76 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (singleton(v0) = v2) | ~ (union(v0, v2) = v3) | ~ (member(v1, v3) = 0) | ? [v4] : (suc(v0) = v4 & member(v1, v4) = 0))
% 9.50/2.76 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (initial_segment(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | (apply(v1, v3, v0) = 0 & member(v3, v2) = 0))
% 9.50/2.76 | (105) member(all_0_2_2, on) = 0
% 9.50/2.76 | (106) ! [v0] : ! [v1] : ( ~ (member(v0, v1) = 0) | apply(member_predicate, v0, v1) = 0)
% 9.50/2.76 | (107) ! [v0] : ! [v1] : ( ~ (apply(member_predicate, v0, v1) = 0) | member(v0, v1) = 0)
% 9.50/2.76 | (108) subset(all_0_1_1, all_0_2_2) = all_0_0_0
% 9.50/2.76 | (109) ! [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)))
% 9.50/2.76 | (110) ? [v0] : ? [v1] : singleton(v0) = v1
% 9.50/2.76 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (strict_well_order(v3, v2) = v1) | ~ (strict_well_order(v3, v2) = v0))
% 9.50/2.76 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 9.50/2.76 | (113) ? [v0] : ? [v1] : product(v0) = v1
% 9.50/2.76 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3))
% 9.50/2.76 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 9.50/2.76 |
% 9.50/2.76 | Instantiating formula (29) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_2_2) = all_0_0_0, yields:
% 9.50/2.76 | (116) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_2_2) = v0 & member(all_0_1_1, v0) = v1)
% 9.50/2.76 |
% 9.50/2.76 | Instantiating formula (36) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_2_2) = all_0_0_0, yields:
% 9.50/2.76 | (117) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_2_2) = v1)
% 9.50/2.76 |
% 9.50/2.77 | Instantiating formula (74) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms subset(all_0_1_1, all_0_2_2) = all_0_0_0, member(all_0_2_2, on) = 0, yields:
% 9.50/2.77 | (118) all_0_0_0 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_1_1, all_0_2_2) = v0)
% 9.50/2.77 |
% 9.50/2.77 | Instantiating formula (77) with all_0_2_2 and discharging atoms member(all_0_2_2, on) = 0, yields:
% 9.50/2.77 | (119) strict_well_order(member_predicate, all_0_2_2) = 0 & set(all_0_2_2) = 0
% 9.50/2.77 |
% 9.50/2.77 | Applying alpha-rule on (119) yields:
% 9.50/2.77 | (120) strict_well_order(member_predicate, all_0_2_2) = 0
% 9.50/2.77 | (121) set(all_0_2_2) = 0
% 9.50/2.77 |
% 9.50/2.77 +-Applying beta-rule and splitting (118), into two cases.
% 9.50/2.77 |-Branch one:
% 9.50/2.77 | (122) all_0_0_0 = 0
% 9.50/2.77 |
% 9.50/2.77 | Equations (122) can reduce 88 to:
% 9.50/2.77 | (123) $false
% 9.50/2.77 |
% 9.50/2.77 |-The branch is then unsatisfiable
% 9.50/2.77 |-Branch two:
% 9.50/2.77 | (88) ~ (all_0_0_0 = 0)
% 9.50/2.77 | (125) ? [v0] : ( ~ (v0 = 0) & member(all_0_1_1, all_0_2_2) = v0)
% 9.50/2.77 |
% 9.50/2.77 +-Applying beta-rule and splitting (116), into two cases.
% 9.50/2.77 |-Branch one:
% 9.50/2.77 | (122) all_0_0_0 = 0
% 9.50/2.77 |
% 9.50/2.77 | Equations (122) can reduce 88 to:
% 9.50/2.77 | (123) $false
% 9.50/2.77 |
% 9.50/2.77 |-The branch is then unsatisfiable
% 9.50/2.77 |-Branch two:
% 9.50/2.77 | (88) ~ (all_0_0_0 = 0)
% 9.50/2.77 | (129) ? [v0] : ? [v1] : ( ~ (v1 = 0) & power_set(all_0_2_2) = v0 & member(all_0_1_1, v0) = v1)
% 9.50/2.77 |
% 9.50/2.77 +-Applying beta-rule and splitting (117), into two cases.
% 9.50/2.77 |-Branch one:
% 9.50/2.77 | (122) all_0_0_0 = 0
% 9.50/2.77 |
% 9.50/2.77 | Equations (122) can reduce 88 to:
% 9.50/2.77 | (123) $false
% 9.50/2.77 |
% 9.50/2.77 |-The branch is then unsatisfiable
% 9.50/2.77 |-Branch two:
% 9.50/2.77 | (88) ~ (all_0_0_0 = 0)
% 9.50/2.77 | (133) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_1_1) = 0 & member(v0, all_0_2_2) = v1)
% 9.50/2.77 |
% 9.50/2.77 | Instantiating (133) with all_68_0_59, all_68_1_60 yields:
% 9.50/2.77 | (134) ~ (all_68_0_59 = 0) & member(all_68_1_60, all_0_1_1) = 0 & member(all_68_1_60, all_0_2_2) = all_68_0_59
% 9.50/2.77 |
% 9.50/2.77 | Applying alpha-rule on (134) yields:
% 9.50/2.77 | (135) ~ (all_68_0_59 = 0)
% 9.50/2.77 | (136) member(all_68_1_60, all_0_1_1) = 0
% 9.50/2.77 | (137) member(all_68_1_60, all_0_2_2) = all_68_0_59
% 9.50/2.77 |
% 9.50/2.77 | Instantiating formula (70) with 0, all_0_2_2 and discharging atoms strict_well_order(member_predicate, all_0_2_2) = 0, yields:
% 9.50/2.77 | (138) ? [v0] : ((v0 = 0 & set(all_0_2_2) = 0 & ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v1, all_0_2_2) = v2) | ? [v3] : ( ~ (v3 = 0) & member(v1, all_0_2_2) = v3)) & ! [v1] : ( ~ (member(v1, all_0_2_2) = 0) | subset(v1, all_0_2_2) = 0)) | ( ~ (v0 = 0) & member(all_0_2_2, on) = v0))
% 9.50/2.77 |
% 9.50/2.77 | Instantiating formula (41) with all_0_1_1, all_0_2_2, all_68_1_60 and discharging atoms sum(all_0_2_2) = all_0_1_1, member(all_68_1_60, all_0_1_1) = 0, yields:
% 9.50/2.77 | (139) ? [v0] : (member(v0, all_0_2_2) = 0 & member(all_68_1_60, v0) = 0)
% 9.50/2.77 |
% 9.50/2.77 | Instantiating formula (19) with all_68_0_59, all_0_2_2, all_68_1_60 and discharging atoms member(all_68_1_60, all_0_2_2) = all_68_0_59, yields:
% 9.50/2.77 | (140) all_68_0_59 = 0 | ? [v0] : ( ~ (v0 = 0) & apply(member_predicate, all_68_1_60, all_0_2_2) = v0)
% 9.50/2.77 |
% 9.50/2.77 | Instantiating (139) with all_76_0_61 yields:
% 9.50/2.77 | (141) member(all_76_0_61, all_0_2_2) = 0 & member(all_68_1_60, all_76_0_61) = 0
% 9.50/2.77 |
% 9.50/2.77 | Applying alpha-rule on (141) yields:
% 9.50/2.77 | (142) member(all_76_0_61, all_0_2_2) = 0
% 9.50/2.77 | (143) member(all_68_1_60, all_76_0_61) = 0
% 9.50/2.77 |
% 9.50/2.77 | Instantiating (138) with all_81_0_69 yields:
% 9.50/2.77 | (144) (all_81_0_69 = 0 & set(all_0_2_2) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_0_2_2) = v1) | ? [v2] : ( ~ (v2 = 0) & member(v0, all_0_2_2) = v2)) & ! [v0] : ( ~ (member(v0, all_0_2_2) = 0) | subset(v0, all_0_2_2) = 0)) | ( ~ (all_81_0_69 = 0) & member(all_0_2_2, on) = all_81_0_69)
% 9.50/2.77 |
% 9.50/2.77 +-Applying beta-rule and splitting (144), into two cases.
% 9.50/2.77 |-Branch one:
% 9.50/2.77 | (145) all_81_0_69 = 0 & set(all_0_2_2) = 0 & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_0_2_2) = v1) | ? [v2] : ( ~ (v2 = 0) & member(v0, all_0_2_2) = v2)) & ! [v0] : ( ~ (member(v0, all_0_2_2) = 0) | subset(v0, all_0_2_2) = 0)
% 9.50/2.77 |
% 9.50/2.77 | Applying alpha-rule on (145) yields:
% 9.50/2.77 | (146) all_81_0_69 = 0
% 9.50/2.77 | (121) set(all_0_2_2) = 0
% 9.50/2.77 | (148) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, all_0_2_2) = v1) | ? [v2] : ( ~ (v2 = 0) & member(v0, all_0_2_2) = v2))
% 9.50/2.77 | (149) ! [v0] : ( ~ (member(v0, all_0_2_2) = 0) | subset(v0, all_0_2_2) = 0)
% 9.50/2.77 |
% 9.50/2.77 +-Applying beta-rule and splitting (140), into two cases.
% 9.50/2.77 |-Branch one:
% 9.50/2.77 | (150) all_68_0_59 = 0
% 9.50/2.77 |
% 9.50/2.77 | Equations (150) can reduce 135 to:
% 9.50/2.77 | (123) $false
% 9.50/2.77 |
% 9.50/2.77 |-The branch is then unsatisfiable
% 9.50/2.77 |-Branch two:
% 9.50/2.77 | (135) ~ (all_68_0_59 = 0)
% 9.50/2.77 | (153) ? [v0] : ( ~ (v0 = 0) & apply(member_predicate, all_68_1_60, all_0_2_2) = v0)
% 9.50/2.77 |
% 9.50/2.77 | Instantiating formula (149) with all_76_0_61 and discharging atoms member(all_76_0_61, all_0_2_2) = 0, yields:
% 9.50/2.77 | (154) subset(all_76_0_61, all_0_2_2) = 0
% 9.50/2.77 |
% 9.50/2.77 | Instantiating formula (18) with all_68_1_60, all_0_2_2, all_76_0_61 and discharging atoms subset(all_76_0_61, all_0_2_2) = 0, member(all_68_1_60, all_76_0_61) = 0, yields:
% 9.50/2.77 | (155) member(all_68_1_60, all_0_2_2) = 0
% 9.50/2.77 |
% 9.50/2.77 | Instantiating formula (115) with all_68_0_59, all_68_1_60, all_0_2_2, all_76_0_61 and discharging atoms subset(all_76_0_61, all_0_2_2) = 0, member(all_68_1_60, all_0_2_2) = all_68_0_59, yields:
% 9.50/2.77 | (156) all_68_0_59 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_68_1_60, all_76_0_61) = v0)
% 9.50/2.77 |
% 9.50/2.77 +-Applying beta-rule and splitting (156), into two cases.
% 9.50/2.77 |-Branch one:
% 9.50/2.77 | (150) all_68_0_59 = 0
% 9.50/2.77 |
% 9.50/2.77 | Equations (150) can reduce 135 to:
% 9.50/2.77 | (123) $false
% 9.50/2.77 |
% 9.50/2.77 |-The branch is then unsatisfiable
% 9.50/2.77 |-Branch two:
% 9.50/2.77 | (135) ~ (all_68_0_59 = 0)
% 9.50/2.77 | (160) ? [v0] : ( ~ (v0 = 0) & member(all_68_1_60, all_76_0_61) = v0)
% 9.50/2.77 |
% 9.50/2.77 | Instantiating formula (35) with all_68_1_60, all_0_2_2, 0, all_68_0_59 and discharging atoms member(all_68_1_60, all_0_2_2) = all_68_0_59, member(all_68_1_60, all_0_2_2) = 0, yields:
% 9.50/2.77 | (150) all_68_0_59 = 0
% 9.50/2.77 |
% 9.50/2.77 | Equations (150) can reduce 135 to:
% 9.50/2.77 | (123) $false
% 9.50/2.77 |
% 9.50/2.77 |-The branch is then unsatisfiable
% 9.50/2.77 |-Branch two:
% 9.50/2.77 | (163) ~ (all_81_0_69 = 0) & member(all_0_2_2, on) = all_81_0_69
% 9.50/2.77 |
% 9.50/2.77 | Applying alpha-rule on (163) yields:
% 9.50/2.77 | (164) ~ (all_81_0_69 = 0)
% 9.50/2.77 | (165) member(all_0_2_2, on) = all_81_0_69
% 9.50/2.77 |
% 9.50/2.77 | Instantiating formula (35) with all_0_2_2, on, all_81_0_69, 0 and discharging atoms member(all_0_2_2, on) = all_81_0_69, member(all_0_2_2, on) = 0, yields:
% 9.50/2.77 | (146) all_81_0_69 = 0
% 9.50/2.77 |
% 9.50/2.77 | Equations (146) can reduce 164 to:
% 9.50/2.77 | (123) $false
% 9.50/2.77 |
% 9.50/2.77 |-The branch is then unsatisfiable
% 9.50/2.77 % SZS output end Proof for theBenchmark
% 9.50/2.77
% 9.50/2.77 2187ms
%------------------------------------------------------------------------------