%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU147+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n019.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 08:46:58 EDT 2022

% Result   : Theorem 95.53s 54.35s
% Output   : Proof 104.80s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SEU147+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14  % Command  : ePrincess-casc -timeout=%d %s
% 0.14/0.36  % Computer : n019.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Mon Jun 20 05:04:39 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 0.60/0.62          ____       _                          
% 0.60/0.62    ___  / __ \_____(_)___  ________  __________
% 0.60/0.62   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.62  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.60/0.62  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.60/0.62  
% 0.60/0.62  A Theorem Prover for First-Order Logic
% 0.60/0.62  (ePrincess v.1.0)
% 0.60/0.62  
% 0.60/0.62  (c) Philipp Rümmer, 2009-2015
% 0.60/0.62  (c) Peter Backeman, 2014-2015
% 0.60/0.62  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.62  Bug reports to peter@backeman.se
% 0.60/0.62  
% 0.60/0.62  For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.62  
% 0.60/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.67  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.88/1.01  Prover 0: Preprocessing ...
% 3.29/1.40  Prover 0: Warning: ignoring some quantifiers
% 3.29/1.43  Prover 0: Constructing countermodel ...
% 5.20/1.90  Prover 0: gave up
% 5.20/1.90  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.55/1.95  Prover 1: Preprocessing ...
% 6.30/2.09  Prover 1: Warning: ignoring some quantifiers
% 6.30/2.10  Prover 1: Constructing countermodel ...
% 6.58/2.17  Prover 1: gave up
% 6.58/2.17  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 6.58/2.20  Prover 2: Preprocessing ...
% 7.22/2.36  Prover 2: Warning: ignoring some quantifiers
% 7.22/2.36  Prover 2: Constructing countermodel ...
% 7.83/2.47  Prover 2: gave up
% 7.83/2.47  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 8.15/2.50  Prover 3: Preprocessing ...
% 8.15/2.55  Prover 3: Warning: ignoring some quantifiers
% 8.15/2.56  Prover 3: Constructing countermodel ...
% 9.52/2.82  Prover 3: gave up
% 9.52/2.82  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 9.52/2.85  Prover 4: Preprocessing ...
% 10.28/2.99  Prover 4: Warning: ignoring some quantifiers
% 10.31/3.00  Prover 4: Constructing countermodel ...
% 14.04/3.94  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 14.43/3.99  Prover 5: Preprocessing ...
% 14.66/4.08  Prover 5: Warning: ignoring some quantifiers
% 14.66/4.09  Prover 5: Constructing countermodel ...
% 14.97/4.15  Prover 5: gave up
% 14.97/4.15  Prover 6: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 15.27/4.18  Prover 6: Preprocessing ...
% 15.72/4.27  Prover 6: Warning: ignoring some quantifiers
% 15.72/4.28  Prover 6: Constructing countermodel ...
% 16.01/4.35  Prover 6: gave up
% 16.01/4.35  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 16.01/4.37  Prover 7: Preprocessing ...
% 16.33/4.42  Prover 7: Proving ...
% 40.77/14.10  Prover 8: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 40.87/14.15  Prover 8: Preprocessing ...
% 41.31/14.25  Prover 8: Proving ...
% 95.53/54.35  Prover 7: proved (17334ms)
% 95.53/54.35  Prover 4: stopped
% 95.53/54.35  Prover 8: stopped
% 95.53/54.35  
% 95.53/54.35  % SZS status Theorem for theBenchmark
% 95.53/54.35  
% 95.53/54.35  Generating proof ... found it (size 45)
% 104.06/57.35  
% 104.06/57.35  % SZS output start Proof for theBenchmark
% 104.06/57.35  Assumed formulas after preprocessing and simplification: 
% 104.06/57.35  | (0)  ? [v0] : ( ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (set_difference(v4, v3) = v2) |  ~ (set_difference(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (set_intersection2(v4, v3) = v2) |  ~ (set_intersection2(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (set_union2(v4, v3) = v2) |  ~ (set_union2(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (unordered_pair(v4, v3) = v2) |  ~ (unordered_pair(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (powerset(v3) = v2) |  ~ (powerset(v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (singleton(v3) = v2) |  ~ (singleton(v3) = v1)) &  ? [v1] :  ? [v2] : ( ~ (v2 = v1) & powerset(v0) = v1 & singleton(v0) = v2 & empty(v0) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (set_difference(v4, v6) = v7) |  ~ (singleton(v5) = v6) |  ~ subset(v3, v4) | subset(v3, v7) | in(v5, v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (set_difference(v4, v5) = v7) |  ~ (set_difference(v3, v5) = v6) |  ~ subset(v3, v4) | subset(v6, v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (set_intersection2(v4, v5) = v7) |  ~ (set_intersection2(v3, v5) = v6) |  ~ subset(v3, v4) | subset(v6, v7)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v4 |  ~ (set_difference(v4, v3) = v5) |  ~ (set_union2(v3, v5) = v6) |  ~ subset(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (set_difference(v5, v4) = v6) |  ~ (set_union2(v3, v4) = v5) | set_difference(v3, v4) = v6) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (set_difference(v4, v3) = v5) |  ~ (set_union2(v3, v5) = v6) | set_union2(v3, v4) = v6) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (set_difference(v3, v5) = v6) |  ~ (set_difference(v3, v4) = v5) | set_intersection2(v3, v4) = v6) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (set_intersection2(v4, v5) = v6) |  ~ subset(v3, v5) |  ~ subset(v3, v4) | subset(v3, v6)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (set_union2(v3, v5) = v6) |  ~ subset(v5, v4) |  ~ subset(v3, v4) | subset(v6, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (set_union2(v3, v4) = v5) |  ~ subset(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v3 | v3 = v0 |  ~ (singleton(v4) = v5) |  ~ subset(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v3 |  ~ (set_difference(v3, v4) = v5) |  ~ disjoint(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v3 |  ~ (set_intersection2(v3, v4) = v5) |  ~ subset(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v0 |  ~ (set_difference(v3, v4) = v5) |  ~ subset(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v0 |  ~ (set_intersection2(v3, v4) = v5) |  ~ disjoint(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_difference(v3, v4) = v5) | subset(v5, v3)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_difference(v3, v4) = v5) |  ! [v6] : (v6 = v5 |  ? [v7] : (( ~ in(v7, v6) |  ~ in(v7, v3) | in(v7, v4)) & (in(v7, v6) | (in(v7, v3) &  ~ in(v7, v4)))))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_difference(v3, v4) = v5) | ( ! [v6] : ( ~ in(v6, v5) | (in(v6, v3) &  ~ in(v6, v4))) &  ! [v6] : ( ~ in(v6, v3) | in(v6, v5) | in(v6, v4)))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (singleton(v3) = v5) |  ~ subset(v5, v4) | in(v3, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (singleton(v3) = v5) |  ~ in(v3, v4) | subset(v5, v4)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_intersection2(v3, v4) = v5) |  ~ disjoint(v3, v4) |  ! [v6] :  ~ in(v6, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_intersection2(v3, v4) = v5) | set_intersection2(v4, v3) = v5) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_intersection2(v3, v4) = v5) | disjoint(v3, v4) |  ? [v6] : in(v6, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_intersection2(v3, v4) = v5) | subset(v5, v3)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_intersection2(v3, v4) = v5) |  ! [v6] : (v6 = v5 |  ? [v7] : (( ~ in(v7, v6) |  ~ in(v7, v4) |  ~ in(v7, v3)) & (in(v7, v6) | (in(v7, v4) & in(v7, v3)))))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_intersection2(v3, v4) = v5) | ( ! [v6] : ( ~ in(v6, v5) | (in(v6, v4) & in(v6, v3))) &  ! [v6] : ( ~ in(v6, v4) |  ~ in(v6, v3) | in(v6, v5)))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_union2(v4, v3) = v5) |  ~ empty(v5) | empty(v3)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_union2(v3, v4) = v5) |  ~ empty(v5) | empty(v3)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_union2(v3, v4) = v5) | set_union2(v4, v3) = v5) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_union2(v3, v4) = v5) | subset(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_union2(v3, v4) = v5) |  ! [v6] : (v6 = v5 |  ? [v7] : (( ~ in(v7, v6) | ( ~ in(v7, v4) &  ~ in(v7, v3))) & (in(v7, v6) | in(v7, v4) | in(v7, v3))))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_union2(v3, v4) = v5) | ( ! [v6] : ( ~ in(v6, v5) | in(v6, v4) | in(v6, v3)) &  ! [v6] : (in(v6, v5) | ( ~ in(v6, v4) &  ~ in(v6, v3))))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unordered_pair(v3, v4) = v5) | unordered_pair(v4, v3) = v5) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unordered_pair(v3, v4) = v5) |  ! [v6] : (v6 = v5 |  ? [v7] : ((v7 = v4 | v7 = v3 | in(v7, v6)) & ( ~ in(v7, v6) | ( ~ (v7 = v4) &  ~ (v7 = v3)))))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unordered_pair(v3, v4) = v5) | ( ! [v6] : (v6 = v4 | v6 = v3 |  ~ in(v6, v5)) &  ! [v6] : (in(v6, v5) | ( ~ (v6 = v4) &  ~ (v6 = v3))))) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ disjoint(v4, v5) |  ~ subset(v3, v4) | disjoint(v3, v5)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ subset(v4, v5) |  ~ subset(v3, v4) | subset(v3, v5)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (set_difference(v3, v0) = v4)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (set_intersection2(v3, v3) = v4)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (set_union2(v3, v3) = v4)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (set_union2(v3, v0) = v4)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ empty(v4) |  ~ empty(v3)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ subset(v4, v3) |  ~ subset(v3, v4)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ subset(v3, v4) | proper_subset(v3, v4)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ? [v5] : (( ~ in(v5, v4) |  ~ in(v5, v3)) & (in(v5, v4) | in(v5, v3)))) &  ! [v3] :  ! [v4] : (v4 = v0 |  ~ (set_difference(v0, v3) = v4)) &  ! [v3] :  ! [v4] : (v4 = v0 |  ~ (set_intersection2(v3, v0) = v4)) &  ! [v3] :  ! [v4] : ( ~ (set_difference(v3, v4) = v3) | disjoint(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ (set_difference(v3, v4) = v0) | subset(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ (powerset(v3) = v4) |  ! [v5] : (v5 = v4 |  ? [v6] : (( ~ subset(v6, v3) |  ~ in(v6, v5)) & (subset(v6, v3) | in(v6, v5))))) &  ! [v3] :  ! [v4] : ( ~ (powerset(v3) = v4) | ( ! [v5] : ( ~ subset(v5, v3) | in(v5, v4)) &  ! [v5] : ( ~ in(v5, v4) | subset(v5, v3)))) &  ! [v3] :  ! [v4] : ( ~ (singleton(v3) = v4) |  ! [v5] : (v5 = v4 |  ? [v6] : (( ~ (v6 = v3) |  ~ in(v3, v5)) & (v6 = v3 | in(v6, v5))))) &  ! [v3] :  ! [v4] : ( ~ (singleton(v3) = v4) |  ! [v5] : (subset(v5, v4) | ( ~ (v5 = v4) &  ~ (v5 = v0)))) &  ! [v3] :  ! [v4] : ( ~ (singleton(v3) = v4) | (in(v3, v4) &  ! [v5] : (v5 = v3 |  ~ in(v5, v4)))) &  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v3, v4) = v0) | disjoint(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ (unordered_pair(v3, v3) = v4) | singleton(v3) = v4) &  ! [v3] :  ! [v4] : ( ~ empty(v4) |  ~ in(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ disjoint(v3, v4) | disjoint(v4, v3)) &  ! [v3] :  ! [v4] : ( ~ disjoint(v3, v4) |  ! [v5] : ( ~ in(v5, v4) |  ~ in(v5, v3))) &  ! [v3] :  ! [v4] : ( ~ subset(v3, v4) |  ~ proper_subset(v4, v3)) &  ! [v3] :  ! [v4] : ( ~ subset(v3, v4) |  ! [v5] : ( ~ in(v5, v3) | in(v5, v4))) &  ! [v3] :  ! [v4] : ( ~ proper_subset(v4, v3) |  ~ proper_subset(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ proper_subset(v3, v4) | ( ~ (v4 = v3) & subset(v3, v4))) &  ! [v3] :  ! [v4] : ( ~ in(v4, v3) |  ~ in(v3, v4)) &  ! [v3] :  ! [v4] : (disjoint(v3, v4) |  ? [v5] : (in(v5, v4) & in(v5, v3))) &  ! [v3] :  ! [v4] : (subset(v3, v4) |  ? [v5] : (in(v5, v3) &  ~ in(v5, v4))) &  ! [v3] : (v3 = v0 |  ~ empty(v3)) &  ! [v3] : (v3 = v0 |  ~ subset(v3, v0)) &  ! [v3] : (v3 = v0 |  ? [v4] : in(v4, v3)) &  ! [v3] :  ~ (singleton(v3) = v0) &  ! [v3] :  ~ proper_subset(v3, v3) &  ! [v3] :  ~ in(v3, v0) &  ! [v3] : subset(v3, v3) &  ! [v3] : subset(v0, v3) &  ? [v3] :  ~ empty(v3) &  ? [v3] : empty(v3)))
% 104.36/57.40  | Instantiating (0) with all_0_0_0 yields:
% 104.36/57.40  | (1)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ? [v0] :  ? [v1] : ( ~ (v1 = v0) & powerset(all_0_0_0) = v0 & singleton(all_0_0_0) = v1 & empty(all_0_0_0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (set_difference(v3, v5) = v6) |  ~ (singleton(v4) = v5) |  ~ subset(v2, v3) | subset(v2, v6) | in(v4, v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (set_difference(v3, v4) = v6) |  ~ (set_difference(v2, v4) = v5) |  ~ subset(v2, v3) | subset(v5, v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (set_intersection2(v3, v4) = v6) |  ~ (set_intersection2(v2, v4) = v5) |  ~ subset(v2, v3) | subset(v5, v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v3 |  ~ (set_difference(v3, v2) = v4) |  ~ (set_union2(v2, v4) = v5) |  ~ subset(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_difference(v4, v3) = v5) |  ~ (set_union2(v2, v3) = v4) | set_difference(v2, v3) = v5) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_difference(v3, v2) = v4) |  ~ (set_union2(v2, v4) = v5) | set_union2(v2, v3) = v5) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_difference(v2, v4) = v5) |  ~ (set_difference(v2, v3) = v4) | set_intersection2(v2, v3) = v5) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_intersection2(v3, v4) = v5) |  ~ subset(v2, v4) |  ~ subset(v2, v3) | subset(v2, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_union2(v2, v4) = v5) |  ~ subset(v4, v3) |  ~ subset(v2, v3) | subset(v5, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (set_union2(v2, v3) = v4) |  ~ subset(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v2 | v2 = all_0_0_0 |  ~ (singleton(v3) = v4) |  ~ subset(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v2 |  ~ (set_difference(v2, v3) = v4) |  ~ disjoint(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v2 |  ~ (set_intersection2(v2, v3) = v4) |  ~ subset(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = all_0_0_0 |  ~ (set_difference(v2, v3) = v4) |  ~ subset(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = all_0_0_0 |  ~ (set_intersection2(v2, v3) = v4) |  ~ disjoint(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v2, v3) = v4) | subset(v4, v2)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v2, v3) = v4) |  ! [v5] : (v5 = v4 |  ? [v6] : (( ~ in(v6, v5) |  ~ in(v6, v2) | in(v6, v3)) & (in(v6, v5) | (in(v6, v2) &  ~ in(v6, v3)))))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v2, v3) = v4) | ( ! [v5] : ( ~ in(v5, v4) | (in(v5, v2) &  ~ in(v5, v3))) &  ! [v5] : ( ~ in(v5, v2) | in(v5, v4) | in(v5, v3)))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v2) = v4) |  ~ subset(v4, v3) | in(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v2) = v4) |  ~ in(v2, v3) | subset(v4, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) |  ~ disjoint(v2, v3) |  ! [v5] :  ~ in(v5, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) | set_intersection2(v3, v2) = v4) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) | disjoint(v2, v3) |  ? [v5] : in(v5, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) | subset(v4, v2)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) |  ! [v5] : (v5 = v4 |  ? [v6] : (( ~ in(v6, v5) |  ~ in(v6, v3) |  ~ in(v6, v2)) & (in(v6, v5) | (in(v6, v3) & in(v6, v2)))))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) | ( ! [v5] : ( ~ in(v5, v4) | (in(v5, v3) & in(v5, v2))) &  ! [v5] : ( ~ in(v5, v3) |  ~ in(v5, v2) | in(v5, v4)))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v3, v2) = v4) |  ~ empty(v4) | empty(v2)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v2, v3) = v4) |  ~ empty(v4) | empty(v2)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v2, v3) = v4) | set_union2(v3, v2) = v4) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v2, v3) = v4) | subset(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v2, v3) = v4) |  ! [v5] : (v5 = v4 |  ? [v6] : (( ~ in(v6, v5) | ( ~ in(v6, v3) &  ~ in(v6, v2))) & (in(v6, v5) | in(v6, v3) | in(v6, v2))))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v2, v3) = v4) | ( ! [v5] : ( ~ in(v5, v4) | in(v5, v3) | in(v5, v2)) &  ! [v5] : (in(v5, v4) | ( ~ in(v5, v3) &  ~ in(v5, v2))))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unordered_pair(v2, v3) = v4) | unordered_pair(v3, v2) = v4) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unordered_pair(v2, v3) = v4) |  ! [v5] : (v5 = v4 |  ? [v6] : ((v6 = v3 | v6 = v2 | in(v6, v5)) & ( ~ in(v6, v5) | ( ~ (v6 = v3) &  ~ (v6 = v2)))))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unordered_pair(v2, v3) = v4) | ( ! [v5] : (v5 = v3 | v5 = v2 |  ~ in(v5, v4)) &  ! [v5] : (in(v5, v4) | ( ~ (v5 = v3) &  ~ (v5 = v2))))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ disjoint(v3, v4) |  ~ subset(v2, v3) | disjoint(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ subset(v3, v4) |  ~ subset(v2, v3) | subset(v2, v4)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (set_difference(v2, all_0_0_0) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (set_intersection2(v2, v2) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (set_union2(v2, v2) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (set_union2(v2, all_0_0_0) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ empty(v3) |  ~ empty(v2)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ subset(v3, v2) |  ~ subset(v2, v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ subset(v2, v3) | proper_subset(v2, v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ? [v4] : (( ~ in(v4, v3) |  ~ in(v4, v2)) & (in(v4, v3) | in(v4, v2)))) &  ! [v2] :  ! [v3] : (v3 = all_0_0_0 |  ~ (set_difference(all_0_0_0, v2) = v3)) &  ! [v2] :  ! [v3] : (v3 = all_0_0_0 |  ~ (set_intersection2(v2, all_0_0_0) = v3)) &  ! [v2] :  ! [v3] : ( ~ (set_difference(v2, v3) = v2) | disjoint(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ (set_difference(v2, v3) = all_0_0_0) | subset(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ! [v4] : (v4 = v3 |  ? [v5] : (( ~ subset(v5, v2) |  ~ in(v5, v4)) & (subset(v5, v2) | in(v5, v4))))) &  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) | ( ! [v4] : ( ~ subset(v4, v2) | in(v4, v3)) &  ! [v4] : ( ~ in(v4, v3) | subset(v4, v2)))) &  ! [v2] :  ! [v3] : ( ~ (singleton(v2) = v3) |  ! [v4] : (v4 = v3 |  ? [v5] : (( ~ (v5 = v2) |  ~ in(v2, v4)) & (v5 = v2 | in(v5, v4))))) &  ! [v2] :  ! [v3] : ( ~ (singleton(v2) = v3) |  ! [v4] : (subset(v4, v3) | ( ~ (v4 = v3) &  ~ (v4 = all_0_0_0)))) &  ! [v2] :  ! [v3] : ( ~ (singleton(v2) = v3) | (in(v2, v3) &  ! [v4] : (v4 = v2 |  ~ in(v4, v3)))) &  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v2, v3) = all_0_0_0) | disjoint(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ (unordered_pair(v2, v2) = v3) | singleton(v2) = v3) &  ! [v2] :  ! [v3] : ( ~ empty(v3) |  ~ in(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ disjoint(v2, v3) | disjoint(v3, v2)) &  ! [v2] :  ! [v3] : ( ~ disjoint(v2, v3) |  ! [v4] : ( ~ in(v4, v3) |  ~ in(v4, v2))) &  ! [v2] :  ! [v3] : ( ~ subset(v2, v3) |  ~ proper_subset(v3, v2)) &  ! [v2] :  ! [v3] : ( ~ subset(v2, v3) |  ! [v4] : ( ~ in(v4, v2) | in(v4, v3))) &  ! [v2] :  ! [v3] : ( ~ proper_subset(v3, v2) |  ~ proper_subset(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ proper_subset(v2, v3) | ( ~ (v3 = v2) & subset(v2, v3))) &  ! [v2] :  ! [v3] : ( ~ in(v3, v2) |  ~ in(v2, v3)) &  ! [v2] :  ! [v3] : (disjoint(v2, v3) |  ? [v4] : (in(v4, v3) & in(v4, v2))) &  ! [v2] :  ! [v3] : (subset(v2, v3) |  ? [v4] : (in(v4, v2) &  ~ in(v4, v3))) &  ! [v2] : (v2 = all_0_0_0 |  ~ empty(v2)) &  ! [v2] : (v2 = all_0_0_0 |  ~ subset(v2, all_0_0_0)) &  ! [v2] : (v2 = all_0_0_0 |  ? [v3] : in(v3, v2)) &  ! [v2] :  ~ (singleton(v2) = all_0_0_0) &  ! [v2] :  ~ proper_subset(v2, v2) &  ! [v2] :  ~ in(v2, all_0_0_0) &  ! [v2] : subset(v2, v2) &  ! [v2] : subset(all_0_0_0, v2) &  ? [v2] :  ~ empty(v2) &  ? [v2] : empty(v2))
% 104.36/57.42  |
% 104.36/57.42  | Applying alpha-rule on (1) yields:
% 104.36/57.42  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0))
% 104.36/57.42  | (3)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 104.36/57.42  | (4)  ? [v0] :  ? [v1] : ( ~ (v1 = v0) & powerset(all_0_0_0) = v0 & singleton(all_0_0_0) = v1 & empty(all_0_0_0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (set_difference(v3, v5) = v6) |  ~ (singleton(v4) = v5) |  ~ subset(v2, v3) | subset(v2, v6) | in(v4, v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (set_difference(v3, v4) = v6) |  ~ (set_difference(v2, v4) = v5) |  ~ subset(v2, v3) | subset(v5, v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (set_intersection2(v3, v4) = v6) |  ~ (set_intersection2(v2, v4) = v5) |  ~ subset(v2, v3) | subset(v5, v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v3 |  ~ (set_difference(v3, v2) = v4) |  ~ (set_union2(v2, v4) = v5) |  ~ subset(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_difference(v4, v3) = v5) |  ~ (set_union2(v2, v3) = v4) | set_difference(v2, v3) = v5) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_difference(v3, v2) = v4) |  ~ (set_union2(v2, v4) = v5) | set_union2(v2, v3) = v5) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_difference(v2, v4) = v5) |  ~ (set_difference(v2, v3) = v4) | set_intersection2(v2, v3) = v5) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_intersection2(v3, v4) = v5) |  ~ subset(v2, v4) |  ~ subset(v2, v3) | subset(v2, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (set_union2(v2, v4) = v5) |  ~ subset(v4, v3) |  ~ subset(v2, v3) | subset(v5, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v3 |  ~ (set_union2(v2, v3) = v4) |  ~ subset(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v2 | v2 = all_0_0_0 |  ~ (singleton(v3) = v4) |  ~ subset(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v2 |  ~ (set_difference(v2, v3) = v4) |  ~ disjoint(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v2 |  ~ (set_intersection2(v2, v3) = v4) |  ~ subset(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = all_0_0_0 |  ~ (set_difference(v2, v3) = v4) |  ~ subset(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = all_0_0_0 |  ~ (set_intersection2(v2, v3) = v4) |  ~ disjoint(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v2, v3) = v4) | subset(v4, v2)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v2, v3) = v4) |  ! [v5] : (v5 = v4 |  ? [v6] : (( ~ in(v6, v5) |  ~ in(v6, v2) | in(v6, v3)) & (in(v6, v5) | (in(v6, v2) &  ~ in(v6, v3)))))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v2, v3) = v4) | ( ! [v5] : ( ~ in(v5, v4) | (in(v5, v2) &  ~ in(v5, v3))) &  ! [v5] : ( ~ in(v5, v2) | in(v5, v4) | in(v5, v3)))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v2) = v4) |  ~ subset(v4, v3) | in(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v2) = v4) |  ~ in(v2, v3) | subset(v4, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) |  ~ disjoint(v2, v3) |  ! [v5] :  ~ in(v5, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) | set_intersection2(v3, v2) = v4) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) | disjoint(v2, v3) |  ? [v5] : in(v5, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) | subset(v4, v2)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) |  ! [v5] : (v5 = v4 |  ? [v6] : (( ~ in(v6, v5) |  ~ in(v6, v3) |  ~ in(v6, v2)) & (in(v6, v5) | (in(v6, v3) & in(v6, v2)))))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v2, v3) = v4) | ( ! [v5] : ( ~ in(v5, v4) | (in(v5, v3) & in(v5, v2))) &  ! [v5] : ( ~ in(v5, v3) |  ~ in(v5, v2) | in(v5, v4)))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v3, v2) = v4) |  ~ empty(v4) | empty(v2)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v2, v3) = v4) |  ~ empty(v4) | empty(v2)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v2, v3) = v4) | set_union2(v3, v2) = v4) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v2, v3) = v4) | subset(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v2, v3) = v4) |  ! [v5] : (v5 = v4 |  ? [v6] : (( ~ in(v6, v5) | ( ~ in(v6, v3) &  ~ in(v6, v2))) & (in(v6, v5) | in(v6, v3) | in(v6, v2))))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v2, v3) = v4) | ( ! [v5] : ( ~ in(v5, v4) | in(v5, v3) | in(v5, v2)) &  ! [v5] : (in(v5, v4) | ( ~ in(v5, v3) &  ~ in(v5, v2))))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unordered_pair(v2, v3) = v4) | unordered_pair(v3, v2) = v4) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unordered_pair(v2, v3) = v4) |  ! [v5] : (v5 = v4 |  ? [v6] : ((v6 = v3 | v6 = v2 | in(v6, v5)) & ( ~ in(v6, v5) | ( ~ (v6 = v3) &  ~ (v6 = v2)))))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unordered_pair(v2, v3) = v4) | ( ! [v5] : (v5 = v3 | v5 = v2 |  ~ in(v5, v4)) &  ! [v5] : (in(v5, v4) | ( ~ (v5 = v3) &  ~ (v5 = v2))))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ disjoint(v3, v4) |  ~ subset(v2, v3) | disjoint(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ subset(v3, v4) |  ~ subset(v2, v3) | subset(v2, v4)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (set_difference(v2, all_0_0_0) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (set_intersection2(v2, v2) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (set_union2(v2, v2) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ (set_union2(v2, all_0_0_0) = v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ empty(v3) |  ~ empty(v2)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ subset(v3, v2) |  ~ subset(v2, v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ subset(v2, v3) | proper_subset(v2, v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ? [v4] : (( ~ in(v4, v3) |  ~ in(v4, v2)) & (in(v4, v3) | in(v4, v2)))) &  ! [v2] :  ! [v3] : (v3 = all_0_0_0 |  ~ (set_difference(all_0_0_0, v2) = v3)) &  ! [v2] :  ! [v3] : (v3 = all_0_0_0 |  ~ (set_intersection2(v2, all_0_0_0) = v3)) &  ! [v2] :  ! [v3] : ( ~ (set_difference(v2, v3) = v2) | disjoint(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ (set_difference(v2, v3) = all_0_0_0) | subset(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) |  ! [v4] : (v4 = v3 |  ? [v5] : (( ~ subset(v5, v2) |  ~ in(v5, v4)) & (subset(v5, v2) | in(v5, v4))))) &  ! [v2] :  ! [v3] : ( ~ (powerset(v2) = v3) | ( ! [v4] : ( ~ subset(v4, v2) | in(v4, v3)) &  ! [v4] : ( ~ in(v4, v3) | subset(v4, v2)))) &  ! [v2] :  ! [v3] : ( ~ (singleton(v2) = v3) |  ! [v4] : (v4 = v3 |  ? [v5] : (( ~ (v5 = v2) |  ~ in(v2, v4)) & (v5 = v2 | in(v5, v4))))) &  ! [v2] :  ! [v3] : ( ~ (singleton(v2) = v3) |  ! [v4] : (subset(v4, v3) | ( ~ (v4 = v3) &  ~ (v4 = all_0_0_0)))) &  ! [v2] :  ! [v3] : ( ~ (singleton(v2) = v3) | (in(v2, v3) &  ! [v4] : (v4 = v2 |  ~ in(v4, v3)))) &  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v2, v3) = all_0_0_0) | disjoint(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ (unordered_pair(v2, v2) = v3) | singleton(v2) = v3) &  ! [v2] :  ! [v3] : ( ~ empty(v3) |  ~ in(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ disjoint(v2, v3) | disjoint(v3, v2)) &  ! [v2] :  ! [v3] : ( ~ disjoint(v2, v3) |  ! [v4] : ( ~ in(v4, v3) |  ~ in(v4, v2))) &  ! [v2] :  ! [v3] : ( ~ subset(v2, v3) |  ~ proper_subset(v3, v2)) &  ! [v2] :  ! [v3] : ( ~ subset(v2, v3) |  ! [v4] : ( ~ in(v4, v2) | in(v4, v3))) &  ! [v2] :  ! [v3] : ( ~ proper_subset(v3, v2) |  ~ proper_subset(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ proper_subset(v2, v3) | ( ~ (v3 = v2) & subset(v2, v3))) &  ! [v2] :  ! [v3] : ( ~ in(v3, v2) |  ~ in(v2, v3)) &  ! [v2] :  ! [v3] : (disjoint(v2, v3) |  ? [v4] : (in(v4, v3) & in(v4, v2))) &  ! [v2] :  ! [v3] : (subset(v2, v3) |  ? [v4] : (in(v4, v2) &  ~ in(v4, v3))) &  ! [v2] : (v2 = all_0_0_0 |  ~ empty(v2)) &  ! [v2] : (v2 = all_0_0_0 |  ~ subset(v2, all_0_0_0)) &  ! [v2] : (v2 = all_0_0_0 |  ? [v3] : in(v3, v2)) &  ! [v2] :  ~ (singleton(v2) = all_0_0_0) &  ! [v2] :  ~ proper_subset(v2, v2) &  ! [v2] :  ~ in(v2, all_0_0_0) &  ! [v2] : subset(v2, v2) &  ! [v2] : subset(all_0_0_0, v2) &  ? [v2] :  ~ empty(v2) &  ? [v2] : empty(v2))
% 104.36/57.43  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0))
% 104.36/57.43  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0))
% 104.36/57.43  | (7)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 104.36/57.43  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 104.36/57.43  |
% 104.36/57.43  | Instantiating (4) with all_2_0_1, all_2_1_2 yields:
% 104.36/57.43  | (9)  ~ (all_2_0_1 = all_2_1_2) & powerset(all_0_0_0) = all_2_1_2 & singleton(all_0_0_0) = all_2_0_1 & empty(all_0_0_0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v1, v3) = v4) |  ~ (singleton(v2) = v3) |  ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v1, v2) = v4) |  ~ (set_difference(v0, v2) = v3) |  ~ subset(v0, v1) | subset(v3, v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) |  ~ (set_intersection2(v0, v2) = v3) |  ~ subset(v0, v1) | subset(v3, v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) |  ~ subset(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v2, v1) = v3) |  ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v2) = v3) |  ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) |  ~ subset(v0, v2) |  ~ subset(v0, v1) | subset(v0, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v2) = v3) |  ~ subset(v2, v1) |  ~ subset(v0, v1) | subset(v3, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (set_union2(v0, v1) = v2) |  ~ subset(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 | v0 = all_0_0_0 |  ~ (singleton(v1) = v2) |  ~ subset(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_difference(v0, v1) = v2) |  ~ disjoint(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_intersection2(v0, v1) = v2) |  ~ subset(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = all_0_0_0 |  ~ (set_difference(v0, v1) = v2) |  ~ subset(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = all_0_0_0 |  ~ (set_intersection2(v0, v1) = v2) |  ~ disjoint(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : (( ~ in(v4, v3) |  ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) &  ~ in(v4, v1)))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) &  ~ in(v3, v1))) &  ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (singleton(v0) = v2) |  ~ subset(v2, v1) | in(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (singleton(v0) = v2) |  ~ in(v0, v1) | subset(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ disjoint(v0, v1) |  ! [v3] :  ~ in(v3, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) |  ? [v3] : in(v3, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : (( ~ in(v4, v3) |  ~ in(v4, v1) |  ~ in(v4, v0)) & (in(v4, v3) | (in(v4, v1) & in(v4, v0)))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v1) & in(v3, v0))) &  ! [v3] : ( ~ in(v3, v1) |  ~ in(v3, v0) | in(v3, v2)))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ~ empty(v2) | empty(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ empty(v2) | empty(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : (( ~ in(v4, v3) | ( ~ in(v4, v1) &  ~ in(v4, v0))) & (in(v4, v3) | in(v4, v1) | in(v4, v0))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) &  ! [v3] : (in(v3, v2) | ( ~ in(v3, v1) &  ~ in(v3, v0))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : ((v4 = v1 | v4 = v0 | in(v4, v3)) & ( ~ in(v4, v3) | ( ~ (v4 = v1) &  ~ (v4 = v0)))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ( ! [v3] : (v3 = v1 | v3 = v0 |  ~ in(v3, v2)) &  ! [v3] : (in(v3, v2) | ( ~ (v3 = v1) &  ~ (v3 = v0))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ disjoint(v1, v2) |  ~ subset(v0, v1) | disjoint(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v1, v2) |  ~ subset(v0, v1) | subset(v0, v2)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_difference(v0, all_0_0_0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, all_0_0_0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v0, v1) | proper_subset(v0, v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ? [v2] : (( ~ in(v2, v1) |  ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) &  ! [v0] :  ! [v1] : (v1 = all_0_0_0 |  ~ (set_difference(all_0_0_0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = all_0_0_0 |  ~ (set_intersection2(v0, all_0_0_0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ (set_difference(v0, v1) = all_0_0_0) | subset(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ! [v2] : (v2 = v1 |  ? [v3] : (( ~ subset(v3, v0) |  ~ in(v3, v2)) & (subset(v3, v0) | in(v3, v2))))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | ( ! [v2] : ( ~ subset(v2, v0) | in(v2, v1)) &  ! [v2] : ( ~ in(v2, v1) | subset(v2, v0)))) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ! [v2] : (v2 = v1 |  ? [v3] : (( ~ (v3 = v0) |  ~ in(v0, v2)) & (v3 = v0 | in(v3, v2))))) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ! [v2] : (subset(v2, v1) | ( ~ (v2 = v1) &  ~ (v2 = all_0_0_0)))) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) &  ! [v2] : (v2 = v0 |  ~ in(v2, v1)))) &  ! [v0] :  ! [v1] : ( ~ (set_intersection2(v0, v1) = all_0_0_0) | disjoint(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) &  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ disjoint(v0, v1) |  ! [v2] : ( ~ in(v2, v1) |  ~ in(v2, v0))) &  ! [v0] :  ! [v1] : ( ~ subset(v0, v1) |  ~ proper_subset(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ subset(v0, v1) |  ! [v2] : ( ~ in(v2, v0) | in(v2, v1))) &  ! [v0] :  ! [v1] : ( ~ proper_subset(v1, v0) |  ~ proper_subset(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ proper_subset(v0, v1) | ( ~ (v1 = v0) & subset(v0, v1))) &  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : (disjoint(v0, v1) |  ? [v2] : (in(v2, v1) & in(v2, v0))) &  ! [v0] :  ! [v1] : (subset(v0, v1) |  ? [v2] : (in(v2, v0) &  ~ in(v2, v1))) &  ! [v0] : (v0 = all_0_0_0 |  ~ empty(v0)) &  ! [v0] : (v0 = all_0_0_0 |  ~ subset(v0, all_0_0_0)) &  ! [v0] : (v0 = all_0_0_0 |  ? [v1] : in(v1, v0)) &  ! [v0] :  ~ (singleton(v0) = all_0_0_0) &  ! [v0] :  ~ proper_subset(v0, v0) &  ! [v0] :  ~ in(v0, all_0_0_0) &  ! [v0] : subset(v0, v0) &  ! [v0] : subset(all_0_0_0, v0) &  ? [v0] :  ~ empty(v0) &  ? [v0] : empty(v0)
% 104.36/57.45  |
% 104.36/57.45  | Applying alpha-rule on (9) yields:
% 104.36/57.45  | (10)  ! [v0] :  ! [v1] : ( ~ disjoint(v0, v1) |  ! [v2] : ( ~ in(v2, v1) |  ~ in(v2, v0)))
% 104.36/57.45  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ~ empty(v2) | empty(v0))
% 104.36/57.45  | (12)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_difference(v0, all_0_0_0) = v1))
% 104.36/57.45  | (13)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1))
% 104.36/57.45  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : ((v4 = v1 | v4 = v0 | in(v4, v3)) & ( ~ in(v4, v3) | ( ~ (v4 = v1) &  ~ (v4 = v0))))))
% 104.36/57.45  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) |  ~ subset(v0, v2) |  ~ subset(v0, v1) | subset(v0, v3))
% 104.36/57.45  | (16)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = all_0_0_0 |  ~ (set_difference(v0, v1) = v2) |  ~ subset(v0, v1))
% 104.36/57.45  | (17)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v0) &  ~ in(v3, v1))) &  ! [v3] : ( ~ in(v3, v0) | in(v3, v2) | in(v3, v1))))
% 104.36/57.45  | (18)  ! [v0] :  ! [v1] : (v1 = all_0_0_0 |  ~ (set_intersection2(v0, all_0_0_0) = v1))
% 104.36/57.45  | (19)  ! [v0] :  ! [v1] : (v1 = v0 |  ? [v2] : (( ~ in(v2, v1) |  ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 104.36/57.45  | (20)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (set_union2(v0, v1) = v2) |  ~ subset(v0, v1))
% 104.36/57.45  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ empty(v2) | empty(v0))
% 104.36/57.45  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : (( ~ in(v4, v3) |  ~ in(v4, v0) | in(v4, v1)) & (in(v4, v3) | (in(v4, v0) &  ~ in(v4, v1))))))
% 104.36/57.45  | (23)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) &  ! [v2] : (v2 = v0 |  ~ in(v2, v1))))
% 104.36/57.45  | (24)  ! [v0] : subset(v0, v0)
% 104.36/57.45  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ disjoint(v1, v2) |  ~ subset(v0, v1) | disjoint(v0, v2))
% 104.36/57.45  | (26)  ? [v0] : empty(v0)
% 104.36/57.45  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) &  ! [v3] : (in(v3, v2) | ( ~ in(v3, v1) &  ~ in(v3, v0)))))
% 104.36/57.45  | (28)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 104.36/57.45  | (29)  ! [v0] :  ! [v1] : ( ~ (set_difference(v0, v1) = all_0_0_0) | subset(v0, v1))
% 104.36/57.45  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) |  ~ subset(v0, v1))
% 104.36/57.45  | (31) powerset(all_0_0_0) = all_2_1_2
% 104.36/57.45  | (32)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = all_0_0_0 |  ~ (set_intersection2(v0, v1) = v2) |  ~ disjoint(v0, v1))
% 104.36/57.46  | (33)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1))
% 104.36/57.46  | (34) empty(all_0_0_0)
% 104.36/57.46  | (35)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | ( ! [v2] : ( ~ subset(v2, v0) | in(v2, v1)) &  ! [v2] : ( ~ in(v2, v1) | subset(v2, v0))))
% 104.36/57.46  | (36)  ! [v0] :  ! [v1] : ( ~ subset(v0, v1) |  ~ proper_subset(v1, v0))
% 104.36/57.46  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v1, v2) = v4) |  ~ (set_difference(v0, v2) = v3) |  ~ subset(v0, v1) | subset(v3, v4))
% 104.36/57.46  | (38)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_difference(v0, v1) = v2) |  ~ disjoint(v0, v1))
% 104.36/57.46  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 104.36/57.46  | (40)  ! [v0] : (v0 = all_0_0_0 |  ~ empty(v0))
% 104.36/57.46  | (41)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 104.36/57.46  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v2) = v3) |  ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 104.36/57.46  | (43)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) |  ? [v3] : in(v3, v2))
% 104.36/57.46  | (44)  ! [v0] : (v0 = all_0_0_0 |  ? [v1] : in(v1, v0))
% 104.36/57.46  | (45)  ! [v0] :  ! [v1] : ( ~ (set_intersection2(v0, v1) = all_0_0_0) | disjoint(v0, v1))
% 104.36/57.46  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v2, v1) = v3) |  ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 104.36/57.46  | (47)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ! [v2] : (v2 = v1 |  ? [v3] : (( ~ (v3 = v0) |  ~ in(v0, v2)) & (v3 = v0 | in(v3, v2)))))
% 104.36/57.46  | (48)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0))
% 104.36/57.46  | (49)  ! [v0] :  ! [v1] : ( ~ proper_subset(v0, v1) | ( ~ (v1 = v0) & subset(v0, v1)))
% 104.36/57.46  | (50)  ! [v0] : (v0 = all_0_0_0 |  ~ subset(v0, all_0_0_0))
% 104.36/57.46  | (51)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ! [v2] : (v2 = v1 |  ? [v3] : (( ~ subset(v3, v0) |  ~ in(v3, v2)) & (subset(v3, v0) | in(v3, v2)))))
% 104.36/57.46  | (52)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v1, v2) |  ~ subset(v0, v1) | subset(v0, v2))
% 104.36/57.46  | (53)  ! [v0] :  ~ proper_subset(v0, v0)
% 104.36/57.46  | (54)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2))
% 104.36/57.46  | (55)  ! [v0] :  ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 104.80/57.46  | (56)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
% 104.80/57.46  | (57)  ~ (all_2_0_1 = all_2_1_2)
% 104.80/57.46  | (58)  ? [v0] :  ~ empty(v0)
% 104.80/57.46  | (59)  ! [v0] : subset(all_0_0_0, v0)
% 104.80/57.46  | (60)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 104.80/57.46  | (61)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v0, v1) | proper_subset(v0, v1))
% 104.80/57.46  | (62)  ! [v0] :  ~ in(v0, all_0_0_0)
% 104.80/57.46  | (63)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ( ! [v3] : (v3 = v1 | v3 = v0 |  ~ in(v3, v2)) &  ! [v3] : (in(v3, v2) | ( ~ (v3 = v1) &  ~ (v3 = v0)))))
% 104.80/57.46  | (64)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (singleton(v0) = v2) |  ~ in(v0, v1) | subset(v2, v1))
% 104.80/57.46  | (65)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (singleton(v0) = v2) |  ~ subset(v2, v1) | in(v0, v1))
% 104.80/57.46  | (66)  ! [v0] :  ~ (singleton(v0) = all_0_0_0)
% 104.80/57.46  | (67)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 104.80/57.46  | (68)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 104.80/57.46  | (69)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : (( ~ in(v4, v3) | ( ~ in(v4, v1) &  ~ in(v4, v0))) & (in(v4, v3) | in(v4, v1) | in(v4, v0)))))
% 104.80/57.46  | (70)  ! [v0] :  ! [v1] : (disjoint(v0, v1) |  ? [v2] : (in(v2, v1) & in(v2, v0)))
% 104.80/57.46  | (71)  ! [v0] :  ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1))
% 104.80/57.46  | (72)  ! [v0] :  ! [v1] : (subset(v0, v1) |  ? [v2] : (in(v2, v0) &  ~ in(v2, v1)))
% 104.80/57.46  | (73)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 104.80/57.46  | (74)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_intersection2(v0, v1) = v2) |  ~ subset(v0, v1))
% 104.80/57.46  | (75)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ disjoint(v0, v1) |  ! [v3] :  ~ in(v3, v2))
% 104.80/57.46  | (76)  ! [v0] :  ! [v1] : (v1 = all_0_0_0 |  ~ (set_difference(all_0_0_0, v0) = v1))
% 104.80/57.46  | (77)  ! [v0] :  ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0))
% 104.80/57.46  | (78)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0))
% 104.80/57.46  | (79)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v2) = v3) |  ~ subset(v2, v1) |  ~ subset(v0, v1) | subset(v3, v1))
% 104.80/57.46  | (80)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v1, v3) = v4) |  ~ (singleton(v2) = v3) |  ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0))
% 104.80/57.46  | (81)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, all_0_0_0) = v1))
% 104.80/57.46  | (82)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ! [v2] : (subset(v2, v1) | ( ~ (v2 = v1) &  ~ (v2 = all_0_0_0))))
% 104.80/57.46  | (83)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ( ! [v3] : ( ~ in(v3, v2) | (in(v3, v1) & in(v3, v0))) &  ! [v3] : ( ~ in(v3, v1) |  ~ in(v3, v0) | in(v3, v2))))
% 104.80/57.46  | (84)  ! [v0] :  ! [v1] : ( ~ subset(v0, v1) |  ! [v2] : ( ~ in(v2, v0) | in(v2, v1)))
% 104.80/57.46  | (85)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) |  ~ (set_intersection2(v0, v2) = v3) |  ~ subset(v0, v1) | subset(v3, v4))
% 104.80/57.46  | (86)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 | v0 = all_0_0_0 |  ~ (singleton(v1) = v2) |  ~ subset(v0, v2))
% 104.80/57.46  | (87)  ! [v0] :  ! [v1] : ( ~ proper_subset(v1, v0) |  ~ proper_subset(v0, v1))
% 104.80/57.46  | (88)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : (( ~ in(v4, v3) |  ~ in(v4, v1) |  ~ in(v4, v0)) & (in(v4, v3) | (in(v4, v1) & in(v4, v0))))))
% 104.80/57.47  | (89) singleton(all_0_0_0) = all_2_0_1
% 104.80/57.47  |
% 104.80/57.47  | Instantiating formula (35) with all_2_1_2, all_0_0_0 and discharging atoms powerset(all_0_0_0) = all_2_1_2, yields:
% 104.80/57.47  | (90)  ! [v0] : ( ~ subset(v0, all_0_0_0) | in(v0, all_2_1_2)) &  ! [v0] : ( ~ in(v0, all_2_1_2) | subset(v0, all_0_0_0))
% 104.80/57.47  |
% 104.80/57.47  | Applying alpha-rule on (90) yields:
% 104.80/57.47  | (91)  ! [v0] : ( ~ subset(v0, all_0_0_0) | in(v0, all_2_1_2))
% 104.80/57.47  | (92)  ! [v0] : ( ~ in(v0, all_2_1_2) | subset(v0, all_0_0_0))
% 104.80/57.47  |
% 104.80/57.47  | Instantiating formula (23) with all_2_0_1, all_0_0_0 and discharging atoms singleton(all_0_0_0) = all_2_0_1, yields:
% 104.80/57.47  | (93) in(all_0_0_0, all_2_0_1) &  ! [v0] : (v0 = all_0_0_0 |  ~ in(v0, all_2_0_1))
% 104.80/57.47  |
% 104.80/57.47  | Applying alpha-rule on (93) yields:
% 104.80/57.47  | (94) in(all_0_0_0, all_2_0_1)
% 104.80/57.47  | (95)  ! [v0] : (v0 = all_0_0_0 |  ~ in(v0, all_2_0_1))
% 104.80/57.47  |
% 104.80/57.47  | Instantiating formula (91) with all_0_0_0 yields:
% 104.80/57.47  | (96)  ~ subset(all_0_0_0, all_0_0_0) | in(all_0_0_0, all_2_1_2)
% 104.80/57.47  |
% 104.80/57.47  +-Applying beta-rule and splitting (96), into two cases.
% 104.80/57.47  |-Branch one:
% 104.80/57.47  | (97) in(all_0_0_0, all_2_1_2)
% 104.80/57.47  |
% 104.80/57.47  	| Instantiating formula (64) with all_2_0_1, all_2_1_2, all_0_0_0 and discharging atoms singleton(all_0_0_0) = all_2_0_1, in(all_0_0_0, all_2_1_2), yields:
% 104.80/57.47  	| (98) subset(all_2_0_1, all_2_1_2)
% 104.80/57.47  	|
% 104.80/57.47  	| Instantiating formula (61) with all_2_1_2, all_2_0_1 and discharging atoms subset(all_2_0_1, all_2_1_2), yields:
% 104.80/57.47  	| (99) all_2_0_1 = all_2_1_2 | proper_subset(all_2_0_1, all_2_1_2)
% 104.80/57.47  	|
% 104.80/57.47  	+-Applying beta-rule and splitting (99), into two cases.
% 104.80/57.47  	|-Branch one:
% 104.80/57.47  	| (100) proper_subset(all_2_0_1, all_2_1_2)
% 104.80/57.47  	|
% 104.80/57.47  		| Introducing new symbol ex_126_1_12 defined by:
% 104.80/57.47  		| (101) ex_126_1_12 = all_2_1_2
% 104.80/57.47  		|
% 104.80/57.47  		| Introducing new symbol ex_126_0_11 defined by:
% 104.80/57.47  		| (102) ex_126_0_11 = all_2_0_1
% 104.80/57.47  		|
% 104.80/57.47  		| Instantiating formula (72) with ex_126_0_11, ex_126_1_12 yields:
% 104.80/57.47  		| (103) subset(ex_126_1_12, ex_126_0_11) |  ? [v0] : (in(v0, ex_126_1_12) &  ~ in(v0, ex_126_0_11))
% 104.80/57.47  		|
% 104.80/57.47  		+-Applying beta-rule and splitting (103), into two cases.
% 104.80/57.47  		|-Branch one:
% 104.80/57.47  		| (104) subset(ex_126_1_12, ex_126_0_11)
% 104.80/57.47  		|
% 104.80/57.47  			| Instantiating formula (36) with all_2_0_1, all_2_1_2 and discharging atoms proper_subset(all_2_0_1, all_2_1_2), yields:
% 104.80/57.47  			| (105)  ~ subset(all_2_1_2, all_2_0_1)
% 104.80/57.47  			|
% 104.80/57.47  			| From (101)(102) and (104) follows:
% 104.80/57.47  			| (106) subset(all_2_1_2, all_2_0_1)
% 104.80/57.47  			|
% 104.80/57.47  			| Using (106) and (105) yields:
% 104.80/57.47  			| (107) $false
% 104.80/57.47  			|
% 104.80/57.47  			|-The branch is then unsatisfiable
% 104.80/57.47  		|-Branch two:
% 104.80/57.47  		| (108)  ? [v0] : (in(v0, ex_126_1_12) &  ~ in(v0, ex_126_0_11))
% 104.80/57.47  		|
% 104.80/57.47  			| Instantiating (108) with all_128_0_18 yields:
% 104.80/57.47  			| (109) in(all_128_0_18, ex_126_1_12) &  ~ in(all_128_0_18, ex_126_0_11)
% 104.80/57.47  			|
% 104.80/57.47  			| Applying alpha-rule on (109) yields:
% 104.80/57.47  			| (110) in(all_128_0_18, ex_126_1_12)
% 104.80/57.47  			| (111)  ~ in(all_128_0_18, ex_126_0_11)
% 104.80/57.47  			|
% 104.80/57.47  			| Instantiating formula (95) with all_128_0_18 yields:
% 104.80/57.47  			| (112) all_128_0_18 = all_0_0_0 |  ~ in(all_128_0_18, all_2_0_1)
% 104.80/57.47  			|
% 104.80/57.47  			| Instantiating formula (92) with all_128_0_18 yields:
% 104.80/57.47  			| (113)  ~ in(all_128_0_18, all_2_1_2) | subset(all_128_0_18, all_0_0_0)
% 104.80/57.47  			|
% 104.80/57.47  			+-Applying beta-rule and splitting (112), into two cases.
% 104.80/57.47  			|-Branch one:
% 104.80/57.47  			| (114)  ~ in(all_128_0_18, all_2_0_1)
% 104.80/57.47  			|
% 104.80/57.47  				+-Applying beta-rule and splitting (113), into two cases.
% 104.80/57.47  				|-Branch one:
% 104.80/57.47  				| (115)  ~ in(all_128_0_18, all_2_1_2)
% 104.80/57.47  				|
% 104.80/57.47  					| From (101) and (110) follows:
% 104.80/57.47  					| (116) in(all_128_0_18, all_2_1_2)
% 104.80/57.47  					|
% 104.80/57.47  					| Using (116) and (115) yields:
% 104.80/57.47  					| (107) $false
% 104.80/57.47  					|
% 104.80/57.47  					|-The branch is then unsatisfiable
% 104.80/57.47  				|-Branch two:
% 104.80/57.47  				| (118) subset(all_128_0_18, all_0_0_0)
% 104.80/57.47  				|
% 104.80/57.47  					| Instantiating formula (50) with all_128_0_18 and discharging atoms subset(all_128_0_18, all_0_0_0), yields:
% 104.80/57.47  					| (119) all_128_0_18 = all_0_0_0
% 104.80/57.47  					|
% 104.80/57.47  					| From (119) and (114) follows:
% 104.80/57.47  					| (120)  ~ in(all_0_0_0, all_2_0_1)
% 104.80/57.47  					|
% 104.80/57.47  					| Using (94) and (120) yields:
% 104.80/57.47  					| (107) $false
% 104.80/57.47  					|
% 104.80/57.47  					|-The branch is then unsatisfiable
% 104.80/57.47  			|-Branch two:
% 104.80/57.47  			| (119) all_128_0_18 = all_0_0_0
% 104.80/57.47  			|
% 104.80/57.47  				| From (119) and (111) follows:
% 104.80/57.47  				| (123)  ~ in(all_0_0_0, ex_126_0_11)
% 104.80/57.47  				|
% 104.80/57.47  				| From (102) and (123) follows:
% 104.80/57.47  				| (120)  ~ in(all_0_0_0, all_2_0_1)
% 104.80/57.47  				|
% 104.80/57.47  				| Using (94) and (120) yields:
% 104.80/57.47  				| (107) $false
% 104.80/57.47  				|
% 104.80/57.47  				|-The branch is then unsatisfiable
% 104.80/57.47  	|-Branch two:
% 104.80/57.47  	| (126) all_2_0_1 = all_2_1_2
% 104.80/57.47  	|
% 104.80/57.47  		| Equations (126) can reduce 57 to:
% 104.80/57.47  		| (127) $false
% 104.80/57.47  		|
% 104.80/57.47  		|-The branch is then unsatisfiable
% 104.80/57.47  |-Branch two:
% 104.80/57.47  | (128)  ~ subset(all_0_0_0, all_0_0_0)
% 104.80/57.47  |
% 104.80/57.47  	| Introducing new symbol ex_44_0_28 defined by:
% 104.80/57.47  	| (129) ex_44_0_28 = all_0_0_0
% 104.80/57.47  	|
% 104.80/57.47  	| Instantiating formula (24) with ex_44_0_28 yields:
% 104.80/57.47  	| (130) subset(ex_44_0_28, ex_44_0_28)
% 104.80/57.47  	|
% 104.80/57.47  	| From (129)(129) and (130) follows:
% 104.80/57.47  	| (131) subset(all_0_0_0, all_0_0_0)
% 104.80/57.47  	|
% 104.80/57.47  	| Using (131) and (128) yields:
% 104.80/57.47  	| (107) $false
% 104.80/57.47  	|
% 104.80/57.47  	|-The branch is then unsatisfiable
% 104.80/57.47  % SZS output end Proof for theBenchmark
% 104.80/57.47  
% 104.80/57.47  56840ms
%------------------------------------------------------------------------------