%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET813+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n026.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 4.14s 1.61s
% Output   : Proof 6.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11  % Problem  : SET813+4 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 16:46:56 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.57/0.57          ____       _                          
% 0.57/0.57    ___  / __ \_____(_)___  ________  __________
% 0.57/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.57/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.57/0.57  
% 0.57/0.57  A Theorem Prover for First-Order Logic
% 0.57/0.58  (ePrincess v.1.0)
% 0.57/0.58  
% 0.57/0.58  (c) Philipp Rümmer, 2009-2015
% 0.57/0.58  (c) Peter Backeman, 2014-2015
% 0.57/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.58  Bug reports to peter@backeman.se
% 0.57/0.58  
% 0.57/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.58  
% 0.57/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.73/0.94  Prover 0: Preprocessing ...
% 2.58/1.20  Prover 0: Warning: ignoring some quantifiers
% 2.75/1.23  Prover 0: Constructing countermodel ...
% 4.14/1.61  Prover 0: proved (983ms)
% 4.14/1.61  
% 4.14/1.61  No countermodel exists, formula is valid
% 4.14/1.61  % SZS status Theorem for theBenchmark
% 4.14/1.61  
% 4.14/1.61  Generating proof ... Warning: ignoring some quantifiers
% 5.44/1.89  found it (size 28)
% 5.44/1.89  
% 5.44/1.89  % SZS output start Proof for theBenchmark
% 5.44/1.89  Assumed formulas after preprocessing and simplification: 
% 5.44/1.89  | (0)  ? [v0] :  ? [v1] : (suc(v0) = v1 & member(v0, on) &  ~ member(v0, v1) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v3 = v2 |  ~ (initial_segment(v6, v5, v4) = v3) |  ~ (initial_segment(v6, v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (initial_segment(v2, v3, v4) = v6) |  ~ apply(v3, v5, v2) |  ~ member(v5, v4) | member(v5, v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (initial_segment(v2, v3, v4) = v6) |  ~ member(v5, v6) | apply(v3, v5, v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (initial_segment(v2, v3, v4) = v6) |  ~ member(v5, v6) | member(v5, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ apply(v2, v5, v6) |  ~ apply(v2, v4, v5) |  ~ strict_order(v2, v3) |  ~ member(v6, v3) |  ~ member(v5, v3) |  ~ member(v4, v3) | apply(v2, v4, v6)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = v4 |  ~ least(v4, v2, v3) |  ~ member(v5, v3) | apply(v2, v4, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v2 | v3 = v2 |  ~ (unordered_pair(v3, v4) = v5) |  ~ member(v2, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (unordered_pair(v5, v4) = v3) |  ~ (unordered_pair(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (difference(v5, v4) = v3) |  ~ (difference(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (union(v5, v4) = v3) |  ~ (union(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (intersection(v5, v4) = v3) |  ~ (intersection(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (product(v3) = v4) |  ~ member(v5, v3) |  ~ member(v2, v4) | member(v2, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (sum(v3) = v4) |  ~ member(v5, v3) |  ~ member(v2, v5) | member(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (singleton(v2) = v4) |  ~ (union(v2, v4) = v5) |  ~ member(v3, v5) |  ? [v6] : (suc(v2) = v6 & member(v3, v6))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (difference(v4, v3) = v5) |  ~ member(v2, v5) |  ~ member(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (difference(v4, v3) = v5) |  ~ member(v2, v5) | member(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (difference(v4, v3) = v5) |  ~ member(v2, v4) | member(v2, v5) | member(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (union(v3, v4) = v5) |  ~ member(v2, v5) | member(v2, v4) | member(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (union(v3, v4) = v5) |  ~ member(v2, v4) | member(v2, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (union(v3, v4) = v5) |  ~ member(v2, v3) | member(v2, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection(v3, v4) = v5) |  ~ member(v2, v5) | member(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection(v3, v4) = v5) |  ~ member(v2, v5) | member(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection(v3, v4) = v5) |  ~ member(v2, v4) |  ~ member(v2, v3) | member(v2, v5)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ apply(v2, v5, v4) |  ~ apply(v2, v4, v5) |  ~ strict_order(v2, v3) |  ~ member(v5, v3) |  ~ member(v4, v3)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ strict_well_order(v2, v3) |  ~ member(v5, v4) |  ~ subset(v4, v3) |  ? [v6] : least(v6, v2, v4)) &  ? [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (singleton(v3) = v4) |  ~ (union(v3, v4) = v5) | member(v2, v5) |  ? [v6] : (suc(v3) = v6 &  ~ member(v2, v6))) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (suc(v4) = v3) |  ~ (suc(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (product(v4) = v3) |  ~ (product(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (sum(v4) = v3) |  ~ (sum(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (singleton(v4) = v3) |  ~ (singleton(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (singleton(v3) = v4) |  ~ member(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v2 |  ~ (power_set(v4) = v3) |  ~ (power_set(v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (suc(v2) = v4) |  ~ member(v3, v4) |  ? [v5] :  ? [v6] : (singleton(v2) = v5 & union(v2, v5) = v6 & member(v3, v6))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (sum(v3) = v4) |  ~ member(v2, v4) |  ? [v5] : (member(v5, v3) & member(v2, v5))) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unordered_pair(v3, v2) = v4) | member(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unordered_pair(v2, v3) = v4) | member(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (power_set(v3) = v4) |  ~ member(v2, v4) | subset(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (power_set(v3) = v4) |  ~ subset(v2, v3) | member(v2, v4)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ least(v4, v2, v3) | member(v4, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ member(v4, v2) |  ~ subset(v2, v3) | member(v4, v3)) &  ? [v2] :  ! [v3] :  ! [v4] : ( ~ (suc(v3) = v4) | member(v2, v4) |  ? [v5] :  ? [v6] : (singleton(v3) = v5 & union(v3, v5) = v6 &  ~ member(v2, v6))) &  ? [v2] :  ! [v3] :  ! [v4] : ( ~ (product(v3) = v4) | member(v2, v4) |  ? [v5] : (member(v5, v3) &  ~ member(v2, v5))) &  ? [v2] :  ! [v3] :  ! [v4] : ( ~ member(v4, v3) | least(v4, v2, v3) |  ? [v5] : ( ~ (v5 = v4) & member(v5, v3) &  ~ apply(v2, v4, v5))) &  ! [v2] :  ! [v3] : ( ~ (singleton(v2) = v3) | member(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ apply(member_predicate, v2, v3) | member(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ strict_order(v2, v3) | strict_well_order(v2, v3) |  ? [v4] :  ? [v5] : (member(v5, v4) & subset(v4, v3) &  ! [v6] :  ~ least(v6, v2, v4))) &  ! [v2] :  ! [v3] : ( ~ strict_well_order(v2, v3) | strict_order(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ set(v2) |  ~ member(v3, v2) | set(v3)) &  ! [v2] :  ! [v3] : ( ~ equal_set(v2, v3) | subset(v3, v2)) &  ! [v2] :  ! [v3] : ( ~ equal_set(v2, v3) | subset(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ member(v3, v2) |  ~ member(v2, on) | subset(v3, v2)) &  ! [v2] :  ! [v3] : ( ~ member(v2, v3) | apply(member_predicate, v2, v3)) &  ! [v2] :  ! [v3] : ( ~ subset(v3, v2) |  ~ subset(v2, v3) | equal_set(v2, v3)) &  ! [v2] : ( ~ strict_well_order(member_predicate, v2) |  ~ set(v2) | member(v2, on) |  ? [v3] : (member(v3, v2) &  ~ subset(v3, v2))) &  ! [v2] : ( ~ member(v2, on) | strict_well_order(member_predicate, v2)) &  ! [v2] : ( ~ member(v2, on) | set(v2)) &  ! [v2] :  ~ member(v2, empty_set) &  ? [v2] :  ? [v3] : (strict_order(v2, v3) |  ? [v4] :  ? [v5] :  ? [v6] : ((apply(v2, v5, v6) & apply(v2, v4, v5) & member(v6, v3) & member(v5, v3) & member(v4, v3) &  ~ apply(v2, v4, v6)) | (apply(v2, v5, v4) & apply(v2, v4, v5) & member(v5, v3) & member(v4, v3)))) &  ? [v2] :  ? [v3] : (subset(v2, v3) |  ? [v4] : (member(v4, v2) &  ~ member(v4, v3))))
% 5.85/1.93  | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 5.85/1.93  | (1) suc(all_0_1_1) = all_0_0_0 & member(all_0_1_1, on) &  ~ member(all_0_1_1, all_0_0_0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (initial_segment(v4, v3, v2) = v1) |  ~ (initial_segment(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (initial_segment(v0, v1, v2) = v4) |  ~ apply(v1, v3, v0) |  ~ member(v3, v2) | member(v3, v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (initial_segment(v0, v1, v2) = v4) |  ~ member(v3, v4) | apply(v1, v3, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (initial_segment(v0, v1, v2) = v4) |  ~ member(v3, v4) | member(v3, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ apply(v0, v3, v4) |  ~ apply(v0, v2, v3) |  ~ strict_order(v0, v1) |  ~ member(v4, v1) |  ~ member(v3, v1) |  ~ member(v2, v1) | apply(v0, v2, v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ least(v2, v0, v1) |  ~ member(v3, v1) | apply(v0, v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v0 | v1 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ~ member(v0, v3)) &  ! [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] : ( ~ (product(v1) = v2) |  ~ member(v3, v1) |  ~ member(v0, v2) | member(v0, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sum(v1) = v2) |  ~ member(v3, v1) |  ~ member(v0, v3) | member(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (singleton(v0) = v2) |  ~ (union(v0, v2) = v3) |  ~ member(v1, v3) |  ? [v4] : (suc(v0) = v4 & member(v1, v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v2, v1) = v3) |  ~ member(v0, v3) |  ~ member(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v2, v1) = v3) |  ~ member(v0, v3) | member(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v2, v1) = v3) |  ~ member(v0, v2) | member(v0, v3) | member(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v1, v2) = v3) |  ~ member(v0, v3) | member(v0, v2) | member(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v1, v2) = v3) |  ~ member(v0, v2) | member(v0, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v1, v2) = v3) |  ~ member(v0, v1) | member(v0, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v1, v2) = v3) |  ~ member(v0, v3) | member(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v1, v2) = v3) |  ~ member(v0, v3) | member(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v1, v2) = v3) |  ~ member(v0, v2) |  ~ member(v0, v1) | member(v0, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ apply(v0, v3, v2) |  ~ apply(v0, v2, v3) |  ~ strict_order(v0, v1) |  ~ member(v3, v1) |  ~ member(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ strict_well_order(v0, v1) |  ~ member(v3, v2) |  ~ subset(v2, v1) |  ? [v4] : least(v4, v0, v2)) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (singleton(v1) = v2) |  ~ (union(v1, v2) = v3) | member(v0, v3) |  ? [v4] : (suc(v1) = v4 &  ~ member(v0, v4))) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (suc(v2) = v1) |  ~ (suc(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)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (power_set(v2) = v1) |  ~ (power_set(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (suc(v0) = v2) |  ~ member(v1, v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v3 & union(v0, v3) = v4 & member(v1, v4))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sum(v1) = v2) |  ~ member(v0, v2) |  ? [v3] : (member(v3, v1) & member(v0, v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | member(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (power_set(v1) = v2) |  ~ member(v0, v2) | subset(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (power_set(v1) = v2) |  ~ subset(v0, v1) | member(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ least(v2, v0, v1) | member(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v0) |  ~ subset(v0, v1) | member(v2, v1)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ (suc(v1) = v2) | member(v0, v2) |  ? [v3] :  ? [v4] : (singleton(v1) = v3 & union(v1, v3) = v4 &  ~ member(v0, v4))) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ (product(v1) = v2) | member(v0, v2) |  ? [v3] : (member(v3, v1) &  ~ member(v0, v3))) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v1) | least(v2, v0, v1) |  ? [v3] : ( ~ (v3 = v2) & member(v3, v1) &  ~ apply(v0, v2, v3))) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | member(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ apply(member_predicate, v0, v1) | member(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ strict_order(v0, v1) | strict_well_order(v0, v1) |  ? [v2] :  ? [v3] : (member(v3, v2) & subset(v2, v1) &  ! [v4] :  ~ least(v4, v0, v2))) &  ! [v0] :  ! [v1] : ( ~ strict_well_order(v0, v1) | strict_order(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ set(v0) |  ~ member(v1, v0) | set(v1)) &  ! [v0] :  ! [v1] : ( ~ equal_set(v0, v1) | subset(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ equal_set(v0, v1) | subset(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ member(v1, v0) |  ~ member(v0, on) | subset(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ member(v0, v1) | apply(member_predicate, v0, v1)) &  ! [v0] :  ! [v1] : ( ~ subset(v1, v0) |  ~ subset(v0, v1) | equal_set(v0, v1)) &  ! [v0] : ( ~ strict_well_order(member_predicate, v0) |  ~ set(v0) | member(v0, on) |  ? [v1] : (member(v1, v0) &  ~ subset(v1, v0))) &  ! [v0] : ( ~ member(v0, on) | strict_well_order(member_predicate, v0)) &  ! [v0] : ( ~ member(v0, on) | set(v0)) &  ! [v0] :  ~ member(v0, empty_set) &  ? [v0] :  ? [v1] : (strict_order(v0, v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((apply(v0, v3, v4) & apply(v0, v2, v3) & member(v4, v1) & member(v3, v1) & member(v2, v1) &  ~ apply(v0, v2, v4)) | (apply(v0, v3, v2) & apply(v0, v2, v3) & member(v3, v1) & member(v2, v1)))) &  ? [v0] :  ? [v1] : (subset(v0, v1) |  ? [v2] : (member(v2, v0) &  ~ member(v2, v1)))
% 5.85/1.95  |
% 5.85/1.95  | Applying alpha-rule on (1) yields:
% 5.85/1.95  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (sum(v2) = v1) |  ~ (sum(v2) = v0))
% 5.85/1.95  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v1, v2) = v3) |  ~ member(v0, v3) | member(v0, v2) | member(v0, v1))
% 5.85/1.95  | (4)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ least(v2, v0, v1) | member(v2, v1))
% 5.85/1.95  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ apply(v0, v3, v2) |  ~ apply(v0, v2, v3) |  ~ strict_order(v0, v1) |  ~ member(v3, v1) |  ~ member(v2, v1))
% 5.85/1.95  | (6) suc(all_0_1_1) = all_0_0_0
% 5.85/1.95  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v1, v2) = v3) |  ~ member(v0, v2) | member(v0, v3))
% 5.85/1.95  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v2, v1) = v3) |  ~ member(v0, v2) | member(v0, v3) | member(v0, v1))
% 5.85/1.95  | (9)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (singleton(v1) = v2) |  ~ (union(v1, v2) = v3) | member(v0, v3) |  ? [v4] : (suc(v1) = v4 &  ~ member(v0, v4)))
% 5.85/1.96  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v1, v2) = v3) |  ~ member(v0, v3) | member(v0, v2))
% 5.85/1.96  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (power_set(v1) = v2) |  ~ subset(v0, v1) | member(v0, v2))
% 5.85/1.96  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (power_set(v1) = v2) |  ~ member(v0, v2) | subset(v0, v1))
% 5.85/1.96  | (13)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (suc(v2) = v1) |  ~ (suc(v2) = v0))
% 5.85/1.96  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (singleton(v0) = v2) |  ~ (union(v0, v2) = v3) |  ~ member(v1, v3) |  ? [v4] : (suc(v0) = v4 & member(v1, v4)))
% 5.85/1.96  | (15)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v0) |  ~ subset(v0, v1) | member(v2, v1))
% 5.85/1.96  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0))
% 5.85/1.96  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v1, v2) = v3) |  ~ member(v0, v1) | member(v0, v3))
% 5.85/1.96  | (18)  ? [v0] :  ? [v1] : (subset(v0, v1) |  ? [v2] : (member(v2, v0) &  ~ member(v2, v1)))
% 5.85/1.96  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 5.85/1.96  | (20)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | member(v0, v1))
% 5.85/1.96  | (21)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ (suc(v1) = v2) | member(v0, v2) |  ? [v3] :  ? [v4] : (singleton(v1) = v3 & union(v1, v3) = v4 &  ~ member(v0, v4)))
% 5.85/1.96  | (22)  ! [v0] : ( ~ strict_well_order(member_predicate, v0) |  ~ set(v0) | member(v0, on) |  ? [v1] : (member(v1, v0) &  ~ subset(v1, v0)))
% 5.85/1.96  | (23)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (suc(v0) = v2) |  ~ member(v1, v2) |  ? [v3] :  ? [v4] : (singleton(v0) = v3 & union(v0, v3) = v4 & member(v1, v4)))
% 5.85/1.96  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (initial_segment(v0, v1, v2) = v4) |  ~ member(v3, v4) | apply(v1, v3, v0))
% 5.85/1.96  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (initial_segment(v4, v3, v2) = v1) |  ~ (initial_segment(v4, v3, v2) = v0))
% 5.85/1.96  | (26)  ~ member(all_0_1_1, all_0_0_0)
% 5.85/1.96  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sum(v1) = v2) |  ~ member(v0, v2) |  ? [v3] : (member(v3, v1) & member(v0, v3)))
% 5.85/1.96  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (initial_segment(v0, v1, v2) = v4) |  ~ member(v3, v4) | member(v3, v2))
% 5.85/1.96  | (29)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (power_set(v2) = v1) |  ~ (power_set(v2) = v0))
% 5.85/1.96  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v1, v2) = v3) |  ~ member(v0, v2) |  ~ member(v0, v1) | member(v0, v3))
% 5.85/1.96  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (initial_segment(v0, v1, v2) = v4) |  ~ apply(v1, v3, v0) |  ~ member(v3, v2) | member(v3, v4))
% 5.85/1.96  | (32)  ! [v0] :  ! [v1] : ( ~ equal_set(v0, v1) | subset(v0, v1))
% 5.85/1.97  | (33) member(all_0_1_1, on)
% 5.85/1.97  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0))
% 5.85/1.97  | (35)  ! [v0] : ( ~ member(v0, on) | set(v0))
% 5.85/1.97  | (36)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v0, v2))
% 5.85/1.97  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (sum(v1) = v2) |  ~ member(v3, v1) |  ~ member(v0, v3) | member(v0, v2))
% 5.85/1.97  | (38)  ! [v0] :  ! [v1] : ( ~ equal_set(v0, v1) | subset(v1, v0))
% 5.85/1.97  | (39)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ (product(v1) = v2) | member(v0, v2) |  ? [v3] : (member(v3, v1) &  ~ member(v0, v3)))
% 5.85/1.97  | (40)  ! [v0] :  ! [v1] : ( ~ member(v0, v1) | apply(member_predicate, v0, v1))
% 5.85/1.97  | (41)  ! [v0] :  ! [v1] : ( ~ apply(member_predicate, v0, v1) | member(v0, v1))
% 5.85/1.97  | (42)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (product(v2) = v1) |  ~ (product(v2) = v0))
% 5.85/1.97  | (43)  ! [v0] :  ! [v1] : ( ~ strict_order(v0, v1) | strict_well_order(v0, v1) |  ? [v2] :  ? [v3] : (member(v3, v2) & subset(v2, v1) &  ! [v4] :  ~ least(v4, v0, v2)))
% 5.85/1.97  | (44)  ! [v0] :  ! [v1] : ( ~ subset(v1, v0) |  ~ subset(v0, v1) | equal_set(v0, v1))
% 5.85/1.97  | (45)  ! [v0] :  ! [v1] : ( ~ member(v1, v0) |  ~ member(v0, on) | subset(v1, v0))
% 5.85/1.97  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ strict_well_order(v0, v1) |  ~ member(v3, v2) |  ~ subset(v2, v1) |  ? [v4] : least(v4, v0, v2))
% 5.85/1.97  | (47)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v1) | least(v2, v0, v1) |  ? [v3] : ( ~ (v3 = v2) & member(v3, v1) &  ~ apply(v0, v2, v3)))
% 5.85/1.97  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0))
% 5.85/1.97  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (product(v1) = v2) |  ~ member(v3, v1) |  ~ member(v0, v2) | member(v0, v3))
% 5.85/1.97  | (50)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | member(v0, v2))
% 5.85/1.97  | (51)  ? [v0] :  ? [v1] : (strict_order(v0, v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((apply(v0, v3, v4) & apply(v0, v2, v3) & member(v4, v1) & member(v3, v1) & member(v2, v1) &  ~ apply(v0, v2, v4)) | (apply(v0, v3, v2) & apply(v0, v2, v3) & member(v3, v1) & member(v2, v1))))
% 5.85/1.97  | (52)  ! [v0] : ( ~ member(v0, on) | strict_well_order(member_predicate, v0))
% 5.85/1.97  | (53)  ! [v0] :  ! [v1] : ( ~ set(v0) |  ~ member(v1, v0) | set(v1))
% 5.85/1.97  | (54)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 5.85/1.97  | (55)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v2, v1) = v3) |  ~ member(v0, v3) | member(v0, v2))
% 5.85/1.97  | (56)  ! [v0] :  ~ member(v0, empty_set)
% 5.85/1.97  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v2, v1) = v3) |  ~ member(v0, v3) |  ~ member(v0, v1))
% 5.85/1.97  | (58)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v2 |  ~ least(v2, v0, v1) |  ~ member(v3, v1) | apply(v0, v2, v3))
% 5.85/1.97  | (59)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v0 | v1 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ~ member(v0, v3))
% 5.85/1.97  | (60)  ! [v0] :  ! [v1] : ( ~ strict_well_order(v0, v1) | strict_order(v0, v1))
% 5.85/1.97  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v1, v2) = v3) |  ~ member(v0, v3) | member(v0, v1))
% 5.85/1.98  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ apply(v0, v3, v4) |  ~ apply(v0, v2, v3) |  ~ strict_order(v0, v1) |  ~ member(v4, v1) |  ~ member(v3, v1) |  ~ member(v2, v1) | apply(v0, v2, v4))
% 5.85/1.98  | (63)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v1) = v2) |  ~ member(v0, v2))
% 5.85/1.98  |
% 5.85/1.98  | Instantiating (21) with all_7_0_7 yields:
% 5.85/1.98  | (64)  ! [v0] :  ! [v1] : ( ~ (suc(v0) = v1) | member(all_7_0_7, v1) |  ? [v2] :  ? [v3] : (singleton(v0) = v2 & union(v0, v2) = v3 &  ~ member(all_7_0_7, v3)))
% 5.85/1.98  |
% 5.85/1.98  | Instantiating formula (64) with all_0_0_0, all_0_1_1 and discharging atoms suc(all_0_1_1) = all_0_0_0, yields:
% 5.85/1.98  | (65) member(all_7_0_7, all_0_0_0) |  ? [v0] :  ? [v1] : (singleton(all_0_1_1) = v0 & union(all_0_1_1, v0) = v1 &  ~ member(all_7_0_7, v1))
% 5.85/1.98  |
% 5.85/1.98  +-Applying beta-rule and splitting (65), into two cases.
% 5.85/1.98  |-Branch one:
% 5.85/1.98  | (66) member(all_7_0_7, all_0_0_0)
% 5.85/1.98  |
% 5.85/1.98  	| Instantiating formula (23) with all_0_0_0, all_7_0_7, all_0_1_1 and discharging atoms suc(all_0_1_1) = all_0_0_0, member(all_7_0_7, all_0_0_0), yields:
% 5.85/1.98  	| (67)  ? [v0] :  ? [v1] : (singleton(all_0_1_1) = v0 & union(all_0_1_1, v0) = v1 & member(all_7_0_7, v1))
% 5.85/1.98  	|
% 5.85/1.98  	| Instantiating (67) with all_52_0_10, all_52_1_11 yields:
% 5.85/1.98  	| (68) singleton(all_0_1_1) = all_52_1_11 & union(all_0_1_1, all_52_1_11) = all_52_0_10 & member(all_7_0_7, all_52_0_10)
% 5.85/1.98  	|
% 5.85/1.98  	| Applying alpha-rule on (68) yields:
% 5.85/1.98  	| (69) singleton(all_0_1_1) = all_52_1_11
% 5.85/1.98  	| (70) union(all_0_1_1, all_52_1_11) = all_52_0_10
% 5.85/1.98  	| (71) member(all_7_0_7, all_52_0_10)
% 5.85/1.98  	|
% 5.85/1.98  	| Instantiating formula (20) with all_52_1_11, all_0_1_1 and discharging atoms singleton(all_0_1_1) = all_52_1_11, yields:
% 5.85/1.98  	| (72) member(all_0_1_1, all_52_1_11)
% 5.85/1.98  	|
% 5.85/1.98  	| Instantiating formula (7) with all_52_0_10, all_52_1_11, all_0_1_1, all_0_1_1 and discharging atoms union(all_0_1_1, all_52_1_11) = all_52_0_10, member(all_0_1_1, all_52_1_11), yields:
% 5.85/1.98  	| (73) member(all_0_1_1, all_52_0_10)
% 5.85/1.98  	|
% 5.85/1.98  	| Instantiating formula (14) with all_52_0_10, all_52_1_11, all_0_1_1, all_0_1_1 and discharging atoms singleton(all_0_1_1) = all_52_1_11, union(all_0_1_1, all_52_1_11) = all_52_0_10, member(all_0_1_1, all_52_0_10), yields:
% 5.85/1.98  	| (74)  ? [v0] : (suc(all_0_1_1) = v0 & member(all_0_1_1, v0))
% 5.85/1.98  	|
% 5.85/1.98  	| Instantiating (74) with all_72_0_12 yields:
% 5.85/1.98  	| (75) suc(all_0_1_1) = all_72_0_12 & member(all_0_1_1, all_72_0_12)
% 5.85/1.98  	|
% 5.85/1.98  	| Applying alpha-rule on (75) yields:
% 5.85/1.98  	| (76) suc(all_0_1_1) = all_72_0_12
% 5.85/1.98  	| (77) member(all_0_1_1, all_72_0_12)
% 5.85/1.98  	|
% 5.85/1.98  	| Instantiating formula (13) with all_0_1_1, all_72_0_12, all_0_0_0 and discharging atoms suc(all_0_1_1) = all_72_0_12, suc(all_0_1_1) = all_0_0_0, yields:
% 5.85/1.98  	| (78) all_72_0_12 = all_0_0_0
% 5.85/1.99  	|
% 5.85/1.99  	| From (78) and (77) follows:
% 5.85/1.99  	| (79) member(all_0_1_1, all_0_0_0)
% 6.21/1.99  	|
% 6.21/1.99  	| Using (79) and (26) yields:
% 6.21/1.99  	| (80) $false
% 6.21/1.99  	|
% 6.21/1.99  	|-The branch is then unsatisfiable
% 6.21/1.99  |-Branch two:
% 6.21/1.99  | (81)  ~ member(all_7_0_7, all_0_0_0)
% 6.21/1.99  | (82)  ? [v0] :  ? [v1] : (singleton(all_0_1_1) = v0 & union(all_0_1_1, v0) = v1 &  ~ member(all_7_0_7, v1))
% 6.21/1.99  |
% 6.21/1.99  	| Instantiating (82) with all_46_0_13, all_46_1_14 yields:
% 6.21/1.99  	| (83) singleton(all_0_1_1) = all_46_1_14 & union(all_0_1_1, all_46_1_14) = all_46_0_13 &  ~ member(all_7_0_7, all_46_0_13)
% 6.21/1.99  	|
% 6.21/1.99  	| Applying alpha-rule on (83) yields:
% 6.21/1.99  	| (84) singleton(all_0_1_1) = all_46_1_14
% 6.21/1.99  	| (85) union(all_0_1_1, all_46_1_14) = all_46_0_13
% 6.21/1.99  	| (86)  ~ member(all_7_0_7, all_46_0_13)
% 6.21/1.99  	|
% 6.21/1.99  	| Instantiating formula (20) with all_46_1_14, all_0_1_1 and discharging atoms singleton(all_0_1_1) = all_46_1_14, yields:
% 6.21/1.99  	| (87) member(all_0_1_1, all_46_1_14)
% 6.21/1.99  	|
% 6.21/1.99  	| Instantiating formula (7) with all_46_0_13, all_46_1_14, all_0_1_1, all_0_1_1 and discharging atoms union(all_0_1_1, all_46_1_14) = all_46_0_13, member(all_0_1_1, all_46_1_14), yields:
% 6.21/1.99  	| (88) member(all_0_1_1, all_46_0_13)
% 6.21/1.99  	|
% 6.21/1.99  	| Instantiating formula (14) with all_46_0_13, all_46_1_14, all_0_1_1, all_0_1_1 and discharging atoms singleton(all_0_1_1) = all_46_1_14, union(all_0_1_1, all_46_1_14) = all_46_0_13, member(all_0_1_1, all_46_0_13), yields:
% 6.21/1.99  	| (74)  ? [v0] : (suc(all_0_1_1) = v0 & member(all_0_1_1, v0))
% 6.21/1.99  	|
% 6.21/1.99  	| Instantiating (74) with all_66_0_15 yields:
% 6.21/1.99  	| (90) suc(all_0_1_1) = all_66_0_15 & member(all_0_1_1, all_66_0_15)
% 6.21/1.99  	|
% 6.21/1.99  	| Applying alpha-rule on (90) yields:
% 6.21/1.99  	| (91) suc(all_0_1_1) = all_66_0_15
% 6.21/1.99  	| (92) member(all_0_1_1, all_66_0_15)
% 6.21/1.99  	|
% 6.21/1.99  	| Instantiating formula (13) with all_0_1_1, all_66_0_15, all_0_0_0 and discharging atoms suc(all_0_1_1) = all_66_0_15, suc(all_0_1_1) = all_0_0_0, yields:
% 6.21/1.99  	| (93) all_66_0_15 = all_0_0_0
% 6.21/1.99  	|
% 6.21/1.99  	| From (93) and (92) follows:
% 6.21/1.99  	| (79) member(all_0_1_1, all_0_0_0)
% 6.21/1.99  	|
% 6.21/1.99  	| Using (79) and (26) yields:
% 6.21/1.99  	| (80) $false
% 6.21/1.99  	|
% 6.21/1.99  	|-The branch is then unsatisfiable
% 6.21/1.99  % SZS output end Proof for theBenchmark
% 6.21/1.99  
% 6.21/1.99  1404ms
%------------------------------------------------------------------------------