%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET688+4 : TPTP v8.1.0. Released v2.2.0.
% 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 00:21:25 EDT 2022

% Result   : Theorem 3.55s 1.59s
% Output   : Proof 5.05s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET688+4 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12  % 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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jul 10 21:08:45 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.59/0.59          ____       _                          
% 0.59/0.59    ___  / __ \_____(_)___  ________  __________
% 0.59/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.59/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.59/0.59  
% 0.59/0.59  A Theorem Prover for First-Order Logic
% 0.59/0.60  (ePrincess v.1.0)
% 0.59/0.60  
% 0.59/0.60  (c) Philipp Rümmer, 2009-2015
% 0.59/0.60  (c) Peter Backeman, 2014-2015
% 0.59/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.60  Bug reports to peter@backeman.se
% 0.59/0.60  
% 0.59/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.60  
% 0.59/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.68  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.54/0.97  Prover 0: Preprocessing ...
% 1.94/1.18  Prover 0: Warning: ignoring some quantifiers
% 2.20/1.20  Prover 0: Constructing countermodel ...
% 2.61/1.36  Prover 0: gave up
% 2.61/1.36  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.87/1.38  Prover 1: Preprocessing ...
% 3.39/1.51  Prover 1: Constructing countermodel ...
% 3.55/1.59  Prover 1: proved (231ms)
% 3.55/1.59  
% 3.55/1.59  No countermodel exists, formula is valid
% 3.55/1.59  % SZS status Theorem for theBenchmark
% 3.55/1.59  
% 3.55/1.59  Generating proof ... found it (size 39)
% 4.69/1.87  
% 4.69/1.87  % SZS output start Proof for theBenchmark
% 4.69/1.87  Assumed formulas after preprocessing and simplification: 
% 4.69/1.87  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) &  ~ (v3 = 0) & equal_set(v1, v2) = v4 & equal_set(v0, v2) = 0 & equal_set(v0, v1) = v3 & subset(v1, v2) = 0 & subset(v0, v1) = 0 &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (product(v6) = v7) |  ~ (member(v5, v8) = v9) |  ~ (member(v5, v7) = 0) |  ? [v10] : ( ~ (v10 = 0) & member(v8, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (difference(v7, v6) = v8) |  ~ (member(v5, v8) = v9) |  ? [v10] :  ? [v11] : (member(v5, v7) = v10 & member(v5, v6) = v11 & ( ~ (v10 = 0) | v11 = 0))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (union(v6, v7) = v8) |  ~ (member(v5, v8) = v9) |  ? [v10] :  ? [v11] : ( ~ (v11 = 0) &  ~ (v10 = 0) & member(v5, v7) = v11 & member(v5, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (intersection(v6, v7) = v8) |  ~ (member(v5, v8) = v9) |  ? [v10] :  ? [v11] : (member(v5, v7) = v11 & member(v5, v6) = v10 & ( ~ (v11 = 0) |  ~ (v10 = 0)))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v8 = 0 |  ~ (sum(v6) = v7) |  ~ (member(v5, v9) = 0) |  ~ (member(v5, v7) = v8) |  ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (product(v6) = v7) |  ~ (member(v5, v7) = v8) |  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = 0 & member(v5, v9) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (unordered_pair(v6, v5) = v7) |  ~ (member(v5, v7) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (unordered_pair(v5, v6) = v7) |  ~ (member(v5, v7) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (power_set(v6) = v7) |  ~ (member(v5, v7) = v8) |  ? [v9] : ( ~ (v9 = 0) & subset(v5, v6) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v5 | v6 = v5 |  ~ (unordered_pair(v6, v7) = v8) |  ~ (member(v5, v8) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (unordered_pair(v8, v7) = v6) |  ~ (unordered_pair(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (difference(v8, v7) = v6) |  ~ (difference(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (union(v8, v7) = v6) |  ~ (union(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (intersection(v8, v7) = v6) |  ~ (intersection(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (equal_set(v8, v7) = v6) |  ~ (equal_set(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (subset(v8, v7) = v6) |  ~ (subset(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (member(v8, v7) = v6) |  ~ (member(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (difference(v7, v6) = v8) |  ~ (member(v5, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & member(v5, v7) = 0 & member(v5, v6) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (union(v6, v7) = v8) |  ~ (member(v5, v8) = 0) |  ? [v9] :  ? [v10] : (member(v5, v7) = v10 & member(v5, v6) = v9 & (v10 = 0 | v9 = 0))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection(v6, v7) = v8) |  ~ (member(v5, v8) = 0) | (member(v5, v7) = 0 & member(v5, v6) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (singleton(v5) = v6) |  ~ (member(v5, v6) = v7)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (equal_set(v5, v6) = v7) |  ? [v8] :  ? [v9] : (subset(v6, v5) = v9 & subset(v5, v6) = v8 & ( ~ (v9 = 0) |  ~ (v8 = 0)))) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (subset(v5, v6) = v7) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9 & member(v8, v5) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (product(v7) = v6) |  ~ (product(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (sum(v7) = v6) |  ~ (sum(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (singleton(v7) = v6) |  ~ (singleton(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (singleton(v6) = v7) |  ~ (member(v5, v7) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (power_set(v7) = v6) |  ~ (power_set(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (sum(v6) = v7) |  ~ (member(v5, v7) = 0) |  ? [v8] : (member(v8, v6) = 0 & member(v5, v8) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (power_set(v6) = v7) |  ~ (member(v5, v7) = 0) | subset(v5, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (subset(v5, v6) = 0) |  ~ (member(v7, v5) = 0) | member(v7, v6) = 0) &  ! [v5] :  ! [v6] : ( ~ (equal_set(v5, v6) = 0) | (subset(v6, v5) = 0 & subset(v5, v6) = 0)) &  ! [v5] :  ~ (member(v5, empty_set) = 0))
% 5.05/1.92  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 5.05/1.92  | (1)  ~ (all_0_0_0 = 0) &  ~ (all_0_1_1 = 0) & equal_set(all_0_3_3, all_0_2_2) = all_0_0_0 & equal_set(all_0_4_4, all_0_2_2) = 0 & equal_set(all_0_4_4, all_0_3_3) = all_0_1_1 & subset(all_0_3_3, all_0_2_2) = 0 & subset(all_0_4_4, all_0_3_3) = 0 &  ! [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 |  ~ (difference(v2, v1) = v3) |  ~ (member(v0, v3) = v4) |  ? [v5] :  ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) &  ! [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] :  ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [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] : (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] : (v2 = v0 | v1 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ~ (member(v0, v3) = 0)) &  ! [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] : ( ~ (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] :  ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 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 |  ~ (singleton(v0) = v1) |  ~ (member(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_set(v0, v1) = v2) |  ? [v3] :  ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) &  ! [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] : ( ~ (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(v0, v1) = 0) |  ~ (member(v2, v0) = 0) | member(v2, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0)) &  ! [v0] :  ~ (member(v0, empty_set) = 0)
% 5.05/1.93  |
% 5.05/1.93  | Applying alpha-rule on (1) yields:
% 5.05/1.93  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v0) = v1) |  ~ (member(v0, v1) = v2))
% 5.05/1.93  | (3)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sum(v1) = v2) |  ~ (member(v0, v2) = 0) |  ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 5.05/1.93  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0))
% 5.05/1.93  | (5)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v1) = v2) |  ~ (member(v0, v2) = 0))
% 5.05/1.93  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0))
% 5.05/1.93  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v1, v2) = v3) |  ~ (member(v0, v3) = 0) |  ? [v4] :  ? [v5] : (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0)))
% 5.05/1.93  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 5.05/1.93  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v2, v1) = v3) |  ~ (member(v0, v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 5.05/1.93  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0))
% 5.05/1.93  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (product(v1) = v2) |  ~ (member(v0, v3) = v4) |  ~ (member(v0, v2) = 0) |  ? [v5] : ( ~ (v5 = 0) & member(v3, v1) = v5))
% 5.05/1.93  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (difference(v2, v1) = v3) |  ~ (member(v0, v3) = v4) |  ? [v5] :  ? [v6] : (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 5.05/1.93  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (power_set(v1) = v2) |  ~ (member(v0, v2) = 0) | subset(v0, v1) = 0)
% 5.05/1.93  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0))
% 5.05/1.93  | (15)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 5.05/1.93  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = v4) |  ? [v5] :  ? [v6] : (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0))))
% 5.05/1.93  | (17) subset(all_0_3_3, all_0_2_2) = 0
% 5.05/1.94  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (member(v0, v2) = v3))
% 5.05/1.94  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v1, v0) = v2) |  ~ (member(v0, v2) = v3))
% 5.05/1.94  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 5.05/1.94  | (21)  ! [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))
% 5.05/1.94  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_set(v3, v2) = v1) |  ~ (equal_set(v3, v2) = v0))
% 5.05/1.94  | (23)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 5.05/1.94  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v1, v2) = v3) |  ~ (member(v0, v3) = 0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 5.05/1.94  | (25) equal_set(all_0_4_4, all_0_3_3) = all_0_1_1
% 5.05/1.94  | (26)  ! [v0] :  ! [v1] : ( ~ (equal_set(v0, v1) = 0) | (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 5.05/1.94  | (27)  ~ (all_0_1_1 = 0)
% 5.05/1.94  | (28)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (power_set(v2) = v1) |  ~ (power_set(v2) = v0))
% 5.05/1.94  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 5.05/1.94  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v0 | v1 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ~ (member(v0, v3) = 0))
% 5.05/1.94  | (31)  ! [v0] :  ~ (member(v0, empty_set) = 0)
% 5.05/1.94  | (32)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (sum(v2) = v1) |  ~ (sum(v2) = v0))
% 5.05/1.94  | (33)  ~ (all_0_0_0 = 0)
% 5.05/1.94  | (34) equal_set(all_0_4_4, all_0_2_2) = 0
% 5.05/1.94  | (35)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_set(v0, v1) = v2) |  ? [v3] :  ? [v4] : (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0))))
% 5.05/1.94  | (36) subset(all_0_4_4, all_0_3_3) = 0
% 5.05/1.94  | (37)  ! [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))
% 5.05/1.94  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (power_set(v1) = v2) |  ~ (member(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 5.05/1.94  | (39)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (product(v2) = v1) |  ~ (product(v2) = v0))
% 5.05/1.94  | (40) equal_set(all_0_3_3, all_0_2_2) = all_0_0_0
% 5.05/1.94  | (41)  ! [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))
% 5.05/1.94  |
% 5.05/1.95  | Instantiating formula (35) with all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms equal_set(all_0_3_3, all_0_2_2) = all_0_0_0, yields:
% 5.05/1.95  | (42) all_0_0_0 = 0 |  ? [v0] :  ? [v1] : (subset(all_0_2_2, all_0_3_3) = v1 & subset(all_0_3_3, all_0_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 5.05/1.95  |
% 5.05/1.95  | Instantiating formula (26) with all_0_2_2, all_0_4_4 and discharging atoms equal_set(all_0_4_4, all_0_2_2) = 0, yields:
% 5.05/1.95  | (43) subset(all_0_2_2, all_0_4_4) = 0 & subset(all_0_4_4, all_0_2_2) = 0
% 5.05/1.95  |
% 5.05/1.95  | Applying alpha-rule on (43) yields:
% 5.05/1.95  | (44) subset(all_0_2_2, all_0_4_4) = 0
% 5.05/1.95  | (45) subset(all_0_4_4, all_0_2_2) = 0
% 5.05/1.95  |
% 5.05/1.95  | Instantiating formula (35) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms equal_set(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 5.05/1.95  | (46) all_0_1_1 = 0 |  ? [v0] :  ? [v1] : (subset(all_0_3_3, all_0_4_4) = v1 & subset(all_0_4_4, all_0_3_3) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 5.05/1.95  |
% 5.05/1.95  +-Applying beta-rule and splitting (42), into two cases.
% 5.05/1.95  |-Branch one:
% 5.05/1.95  | (47) all_0_0_0 = 0
% 5.05/1.95  |
% 5.05/1.95  	| Equations (47) can reduce 33 to:
% 5.05/1.95  	| (48) $false
% 5.05/1.95  	|
% 5.05/1.95  	|-The branch is then unsatisfiable
% 5.05/1.95  |-Branch two:
% 5.05/1.95  | (33)  ~ (all_0_0_0 = 0)
% 5.05/1.95  | (50)  ? [v0] :  ? [v1] : (subset(all_0_2_2, all_0_3_3) = v1 & subset(all_0_3_3, all_0_2_2) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 5.05/1.95  |
% 5.05/1.95  	| Instantiating (50) with all_13_0_5, all_13_1_6 yields:
% 5.05/1.95  	| (51) subset(all_0_2_2, all_0_3_3) = all_13_0_5 & subset(all_0_3_3, all_0_2_2) = all_13_1_6 & ( ~ (all_13_0_5 = 0) |  ~ (all_13_1_6 = 0))
% 5.05/1.95  	|
% 5.05/1.95  	| Applying alpha-rule on (51) yields:
% 5.05/1.95  	| (52) subset(all_0_2_2, all_0_3_3) = all_13_0_5
% 5.05/1.95  	| (53) subset(all_0_3_3, all_0_2_2) = all_13_1_6
% 5.05/1.95  	| (54)  ~ (all_13_0_5 = 0) |  ~ (all_13_1_6 = 0)
% 5.05/1.95  	|
% 5.05/1.95  	+-Applying beta-rule and splitting (46), into two cases.
% 5.05/1.95  	|-Branch one:
% 5.05/1.95  	| (55) all_0_1_1 = 0
% 5.05/1.95  	|
% 5.05/1.95  		| Equations (55) can reduce 27 to:
% 5.05/1.95  		| (48) $false
% 5.05/1.95  		|
% 5.05/1.95  		|-The branch is then unsatisfiable
% 5.05/1.95  	|-Branch two:
% 5.05/1.95  	| (27)  ~ (all_0_1_1 = 0)
% 5.05/1.95  	| (58)  ? [v0] :  ? [v1] : (subset(all_0_3_3, all_0_4_4) = v1 & subset(all_0_4_4, all_0_3_3) = v0 & ( ~ (v1 = 0) |  ~ (v0 = 0)))
% 5.05/1.95  	|
% 5.05/1.95  		| Instantiating (58) with all_18_0_7, all_18_1_8 yields:
% 5.05/1.95  		| (59) subset(all_0_3_3, all_0_4_4) = all_18_0_7 & subset(all_0_4_4, all_0_3_3) = all_18_1_8 & ( ~ (all_18_0_7 = 0) |  ~ (all_18_1_8 = 0))
% 5.05/1.95  		|
% 5.05/1.95  		| Applying alpha-rule on (59) yields:
% 5.05/1.95  		| (60) subset(all_0_3_3, all_0_4_4) = all_18_0_7
% 5.05/1.95  		| (61) subset(all_0_4_4, all_0_3_3) = all_18_1_8
% 5.05/1.95  		| (62)  ~ (all_18_0_7 = 0) |  ~ (all_18_1_8 = 0)
% 5.05/1.95  		|
% 5.05/1.95  		| Instantiating formula (29) with all_0_3_3, all_0_2_2, all_13_1_6, 0 and discharging atoms subset(all_0_3_3, all_0_2_2) = all_13_1_6, subset(all_0_3_3, all_0_2_2) = 0, yields:
% 5.05/1.95  		| (63) all_13_1_6 = 0
% 5.05/1.95  		|
% 5.05/1.95  		| Instantiating formula (29) with all_0_4_4, all_0_3_3, all_18_1_8, 0 and discharging atoms subset(all_0_4_4, all_0_3_3) = all_18_1_8, subset(all_0_4_4, all_0_3_3) = 0, yields:
% 5.05/1.95  		| (64) all_18_1_8 = 0
% 5.05/1.95  		|
% 5.05/1.95  		| From (64) and (61) follows:
% 5.05/1.95  		| (36) subset(all_0_4_4, all_0_3_3) = 0
% 5.05/1.95  		|
% 5.05/1.96  		+-Applying beta-rule and splitting (54), into two cases.
% 5.05/1.96  		|-Branch one:
% 5.05/1.96  		| (66)  ~ (all_13_0_5 = 0)
% 5.05/1.96  		|
% 5.05/1.96  			| Instantiating formula (23) with all_13_0_5, all_0_3_3, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_3_3) = all_13_0_5, yields:
% 5.05/1.96  			| (67) all_13_0_5 = 0 |  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = 0 & member(v0, all_0_3_3) = v1)
% 5.05/1.96  			|
% 5.05/1.96  			+-Applying beta-rule and splitting (67), into two cases.
% 5.05/1.96  			|-Branch one:
% 5.05/1.96  			| (68) all_13_0_5 = 0
% 5.05/1.96  			|
% 5.05/1.96  				| Equations (68) can reduce 66 to:
% 5.05/1.96  				| (48) $false
% 5.05/1.96  				|
% 5.05/1.96  				|-The branch is then unsatisfiable
% 5.05/1.96  			|-Branch two:
% 5.05/1.96  			| (66)  ~ (all_13_0_5 = 0)
% 5.05/1.96  			| (71)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = 0 & member(v0, all_0_3_3) = v1)
% 5.05/1.96  			|
% 5.05/1.96  				| Instantiating (71) with all_43_0_9, all_43_1_10 yields:
% 5.05/1.96  				| (72)  ~ (all_43_0_9 = 0) & member(all_43_1_10, all_0_2_2) = 0 & member(all_43_1_10, all_0_3_3) = all_43_0_9
% 5.05/1.96  				|
% 5.05/1.96  				| Applying alpha-rule on (72) yields:
% 5.05/1.96  				| (73)  ~ (all_43_0_9 = 0)
% 5.05/1.96  				| (74) member(all_43_1_10, all_0_2_2) = 0
% 5.05/1.96  				| (75) member(all_43_1_10, all_0_3_3) = all_43_0_9
% 5.05/1.96  				|
% 5.05/1.96  				| Instantiating formula (10) with all_43_1_10, all_0_3_3, all_43_0_9, 0 and discharging atoms member(all_43_1_10, all_0_3_3) = all_43_0_9, yields:
% 5.05/1.96  				| (76) all_43_0_9 = 0 |  ~ (member(all_43_1_10, all_0_3_3) = 0)
% 5.05/1.96  				|
% 5.05/1.96  				| Instantiating formula (15) with all_43_1_10, all_0_4_4, all_0_2_2 and discharging atoms subset(all_0_2_2, all_0_4_4) = 0, member(all_43_1_10, all_0_2_2) = 0, yields:
% 5.05/1.96  				| (77) member(all_43_1_10, all_0_4_4) = 0
% 5.05/1.96  				|
% 5.05/1.96  				| Instantiating formula (15) with all_43_1_10, all_0_3_3, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_3_3) = 0, yields:
% 5.05/1.96  				| (78)  ~ (member(all_43_1_10, all_0_4_4) = 0) | member(all_43_1_10, all_0_3_3) = 0
% 5.05/1.96  				|
% 5.05/1.96  				+-Applying beta-rule and splitting (78), into two cases.
% 5.05/1.96  				|-Branch one:
% 5.05/1.96  				| (79)  ~ (member(all_43_1_10, all_0_4_4) = 0)
% 5.05/1.96  				|
% 5.05/1.96  					| Using (77) and (79) yields:
% 5.05/1.96  					| (80) $false
% 5.05/1.96  					|
% 5.05/1.96  					|-The branch is then unsatisfiable
% 5.05/1.96  				|-Branch two:
% 5.05/1.96  				| (77) member(all_43_1_10, all_0_4_4) = 0
% 5.05/1.96  				| (82) member(all_43_1_10, all_0_3_3) = 0
% 5.05/1.96  				|
% 5.05/1.96  					+-Applying beta-rule and splitting (76), into two cases.
% 5.05/1.96  					|-Branch one:
% 5.05/1.96  					| (83)  ~ (member(all_43_1_10, all_0_3_3) = 0)
% 5.05/1.96  					|
% 5.05/1.96  						| Using (82) and (83) yields:
% 5.05/1.96  						| (80) $false
% 5.05/1.96  						|
% 5.05/1.96  						|-The branch is then unsatisfiable
% 5.05/1.96  					|-Branch two:
% 5.05/1.96  					| (82) member(all_43_1_10, all_0_3_3) = 0
% 5.05/1.96  					| (86) all_43_0_9 = 0
% 5.05/1.96  					|
% 5.05/1.96  						| Equations (86) can reduce 73 to:
% 5.05/1.96  						| (48) $false
% 5.05/1.96  						|
% 5.05/1.96  						|-The branch is then unsatisfiable
% 5.05/1.96  		|-Branch two:
% 5.05/1.96  		| (68) all_13_0_5 = 0
% 5.05/1.96  		| (89)  ~ (all_13_1_6 = 0)
% 5.05/1.96  		|
% 5.05/1.96  			| Equations (63) can reduce 89 to:
% 5.05/1.96  			| (48) $false
% 5.05/1.96  			|
% 5.05/1.96  			|-The branch is then unsatisfiable
% 5.05/1.96  % SZS output end Proof for theBenchmark
% 5.05/1.96  
% 5.05/1.96  1350ms
%------------------------------------------------------------------------------