TSTP Solution File: SEU128+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU128+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n027.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 08:46:47 EDT 2022

% Result   : Theorem 2.97s 1.44s
% Output   : Proof 4.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU128+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n027.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 Jun 19 22:10:09 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.58          ____       _                          
% 0.19/0.58    ___  / __ \_____(_)___  ________  __________
% 0.19/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.58  
% 0.19/0.58  A Theorem Prover for First-Order Logic
% 0.19/0.58  (ePrincess v.1.0)
% 0.19/0.58  
% 0.19/0.58  (c) Philipp Rümmer, 2009-2015
% 0.19/0.58  (c) Peter Backeman, 2014-2015
% 0.19/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58  Bug reports to peter@backeman.se
% 0.19/0.58  
% 0.19/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58  
% 0.19/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.76/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.91  Prover 0: Preprocessing ...
% 1.70/1.06  Prover 0: Warning: ignoring some quantifiers
% 1.86/1.08  Prover 0: Constructing countermodel ...
% 2.35/1.26  Prover 0: gave up
% 2.35/1.26  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.35/1.28  Prover 1: Preprocessing ...
% 2.72/1.35  Prover 1: Warning: ignoring some quantifiers
% 2.72/1.35  Prover 1: Constructing countermodel ...
% 2.97/1.44  Prover 1: proved (185ms)
% 2.97/1.44  
% 2.97/1.44  No countermodel exists, formula is valid
% 2.97/1.44  % SZS status Theorem for theBenchmark
% 2.97/1.44  
% 2.97/1.44  Generating proof ... Warning: ignoring some quantifiers
% 4.15/1.76  found it (size 33)
% 4.15/1.76  
% 4.15/1.76  % SZS output start Proof for theBenchmark
% 4.15/1.76  Assumed formulas after preprocessing and simplification: 
% 4.15/1.76  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : ( ~ (v6 = 0) &  ~ (v4 = 0) & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & subset(v0, v3) = v4 & subset(v0, v2) = 0 & subset(v0, v1) = 0 & set_intersection2(v1, v2) = v3 &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (set_intersection2(v8, v9) = v10) |  ~ (in(v11, v8) = v12) |  ? [v13] :  ? [v14] : (in(v11, v10) = v13 & in(v11, v9) = v14 & ( ~ (v13 = 0) | (v14 = 0 & v12 = 0)))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (subset(v11, v10) = v9) |  ~ (subset(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (set_intersection2(v11, v10) = v9) |  ~ (set_intersection2(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (in(v11, v10) = v9) |  ~ (in(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) |  ~ (in(v11, v8) = 0) |  ? [v12] :  ? [v13] : (in(v11, v10) = v13 & in(v11, v9) = v12 & ( ~ (v12 = 0) | v13 = 0))) &  ? [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v8 |  ~ (set_intersection2(v9, v10) = v11) |  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (in(v12, v10) = v15 & in(v12, v9) = v14 & in(v12, v8) = v13 & ( ~ (v15 = 0) |  ~ (v14 = 0) |  ~ (v13 = 0)) & (v13 = 0 | (v15 = 0 & v14 = 0)))) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (subset(v8, v9) = v10) |  ? [v11] :  ? [v12] : ( ~ (v12 = 0) & in(v11, v9) = v12 & in(v11, v8) = 0)) &  ! [v8] :  ! [v9] :  ! [v10] : (v9 = v8 |  ~ (empty(v10) = v9) |  ~ (empty(v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (subset(v8, v9) = 0) |  ~ (in(v10, v8) = 0) | in(v10, v9) = 0) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | set_intersection2(v9, v8) = v10) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (empty(v9) = 0) |  ~ (empty(v8) = 0)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (set_intersection2(v8, v8) = v9)) &  ! [v8] :  ! [v9] : (v9 = empty_set |  ~ (set_intersection2(v8, empty_set) = v9)) &  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (subset(v8, v8) = v9)) &  ! [v8] :  ! [v9] : ( ~ (in(v8, v9) = 0) |  ? [v10] : ( ~ (v10 = 0) & empty(v9) = v10)) &  ! [v8] :  ! [v9] : ( ~ (in(v8, v9) = 0) |  ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)) &  ! [v8] : (v8 = empty_set |  ~ (empty(v8) = 0)))
% 4.50/1.80  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 4.50/1.80  | (1)  ~ (all_0_1_1 = 0) &  ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & subset(all_0_7_7, all_0_4_4) = all_0_3_3 & subset(all_0_7_7, all_0_5_5) = 0 & subset(all_0_7_7, all_0_6_6) = 0 & set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(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 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = 0) |  ? [v4] :  ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) | in(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) &  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0))
% 4.50/1.81  |
% 4.50/1.81  | Applying alpha-rule on (1) yields:
% 4.50/1.81  | (2) subset(all_0_7_7, all_0_6_6) = 0
% 4.50/1.81  | (3)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1))
% 4.50/1.81  | (4) subset(all_0_7_7, all_0_4_4) = all_0_3_3
% 4.50/1.81  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 4.50/1.81  | (6)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 4.50/1.81  | (7)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0))
% 4.50/1.81  | (8)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 4.50/1.81  | (9) set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4
% 4.50/1.81  | (10)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 4.50/1.81  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 4.50/1.81  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 4.50/1.81  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = 0) |  ? [v4] :  ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 4.50/1.81  | (14)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1))
% 4.50/1.81  | (15)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 4.50/1.81  | (16)  ~ (all_0_3_3 = 0)
% 4.50/1.81  | (17) empty(all_0_0_0) = 0
% 4.50/1.81  | (18)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1))
% 4.50/1.81  | (19) empty(all_0_2_2) = all_0_1_1
% 4.50/1.81  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 4.50/1.82  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 4.50/1.82  | (22)  ~ (all_0_1_1 = 0)
% 4.50/1.82  | (23)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 4.50/1.82  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0))
% 4.50/1.82  | (25) empty(empty_set) = 0
% 4.50/1.82  | (26)  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0))
% 4.50/1.82  | (27) subset(all_0_7_7, all_0_5_5) = 0
% 4.50/1.82  |
% 4.50/1.82  | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_4_4) = all_0_3_3, yields:
% 4.50/1.82  | (28) all_0_3_3 = 0 |  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_7_7) = 0)
% 4.50/1.82  |
% 4.50/1.82  | Instantiating formula (21) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 4.50/1.82  | (29) set_intersection2(all_0_5_5, all_0_6_6) = all_0_4_4
% 4.50/1.82  |
% 4.50/1.82  +-Applying beta-rule and splitting (28), into two cases.
% 4.50/1.82  |-Branch one:
% 4.50/1.82  | (30) all_0_3_3 = 0
% 4.50/1.82  |
% 4.50/1.82  	| Equations (30) can reduce 16 to:
% 4.50/1.82  	| (31) $false
% 4.50/1.82  	|
% 4.50/1.82  	|-The branch is then unsatisfiable
% 4.50/1.82  |-Branch two:
% 4.50/1.82  | (16)  ~ (all_0_3_3 = 0)
% 4.50/1.82  | (33)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = v1 & in(v0, all_0_7_7) = 0)
% 4.50/1.82  |
% 4.50/1.82  	| Instantiating (33) with all_27_0_9, all_27_1_10 yields:
% 4.50/1.82  	| (34)  ~ (all_27_0_9 = 0) & in(all_27_1_10, all_0_4_4) = all_27_0_9 & in(all_27_1_10, all_0_7_7) = 0
% 4.50/1.82  	|
% 4.50/1.82  	| Applying alpha-rule on (34) yields:
% 4.50/1.82  	| (35)  ~ (all_27_0_9 = 0)
% 4.50/1.82  	| (36) in(all_27_1_10, all_0_4_4) = all_27_0_9
% 4.50/1.82  	| (37) in(all_27_1_10, all_0_7_7) = 0
% 4.50/1.82  	|
% 4.50/1.82  	| Instantiating formula (20) with all_27_1_10, all_0_5_5, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_5_5) = 0, in(all_27_1_10, all_0_7_7) = 0, yields:
% 4.50/1.82  	| (38) in(all_27_1_10, all_0_5_5) = 0
% 4.50/1.82  	|
% 4.50/1.82  	| Instantiating formula (20) with all_27_1_10, all_0_6_6, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_6_6) = 0, in(all_27_1_10, all_0_7_7) = 0, yields:
% 4.50/1.82  	| (39) in(all_27_1_10, all_0_6_6) = 0
% 4.50/1.82  	|
% 4.50/1.82  	| Instantiating formula (5) with all_27_1_10, all_0_6_6, 0, all_27_0_9 and discharging atoms in(all_27_1_10, all_0_6_6) = 0, yields:
% 4.50/1.82  	| (40) all_27_0_9 = 0 |  ~ (in(all_27_1_10, all_0_6_6) = all_27_0_9)
% 4.50/1.82  	|
% 4.50/1.82  	| Instantiating formula (13) with all_27_1_10, all_0_4_4, all_0_6_6, all_0_5_5 and discharging atoms set_intersection2(all_0_5_5, all_0_6_6) = all_0_4_4, in(all_27_1_10, all_0_5_5) = 0, yields:
% 4.50/1.82  	| (41)  ? [v0] :  ? [v1] : (in(all_27_1_10, all_0_4_4) = v1 & in(all_27_1_10, all_0_6_6) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 4.50/1.82  	|
% 4.50/1.82  	| Instantiating formula (13) with all_27_1_10, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms set_intersection2(all_0_6_6, all_0_5_5) = all_0_4_4, in(all_27_1_10, all_0_6_6) = 0, yields:
% 4.50/1.82  	| (42)  ? [v0] :  ? [v1] : (in(all_27_1_10, all_0_4_4) = v1 & in(all_27_1_10, all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 4.50/1.82  	|
% 4.50/1.82  	| Instantiating (41) with all_60_0_15, all_60_1_16 yields:
% 4.50/1.82  	| (43) in(all_27_1_10, all_0_4_4) = all_60_0_15 & in(all_27_1_10, all_0_6_6) = all_60_1_16 & ( ~ (all_60_1_16 = 0) | all_60_0_15 = 0)
% 4.50/1.83  	|
% 4.50/1.83  	| Applying alpha-rule on (43) yields:
% 4.50/1.83  	| (44) in(all_27_1_10, all_0_4_4) = all_60_0_15
% 4.50/1.83  	| (45) in(all_27_1_10, all_0_6_6) = all_60_1_16
% 4.50/1.83  	| (46)  ~ (all_60_1_16 = 0) | all_60_0_15 = 0
% 4.50/1.83  	|
% 4.50/1.83  	| Instantiating (42) with all_66_0_19, all_66_1_20 yields:
% 4.50/1.83  	| (47) in(all_27_1_10, all_0_4_4) = all_66_0_19 & in(all_27_1_10, all_0_5_5) = all_66_1_20 & ( ~ (all_66_1_20 = 0) | all_66_0_19 = 0)
% 4.50/1.83  	|
% 4.50/1.83  	| Applying alpha-rule on (47) yields:
% 4.50/1.83  	| (48) in(all_27_1_10, all_0_4_4) = all_66_0_19
% 4.50/1.83  	| (49) in(all_27_1_10, all_0_5_5) = all_66_1_20
% 4.50/1.83  	| (50)  ~ (all_66_1_20 = 0) | all_66_0_19 = 0
% 4.50/1.83  	|
% 4.50/1.83  	+-Applying beta-rule and splitting (40), into two cases.
% 4.50/1.83  	|-Branch one:
% 4.50/1.83  	| (51)  ~ (in(all_27_1_10, all_0_6_6) = all_27_0_9)
% 4.50/1.83  	|
% 4.50/1.83  		| Instantiating formula (5) with all_27_1_10, all_0_4_4, all_66_0_19, all_27_0_9 and discharging atoms in(all_27_1_10, all_0_4_4) = all_66_0_19, in(all_27_1_10, all_0_4_4) = all_27_0_9, yields:
% 4.50/1.83  		| (52) all_66_0_19 = all_27_0_9
% 4.50/1.83  		|
% 4.50/1.83  		| Instantiating formula (5) with all_27_1_10, all_0_5_5, all_66_1_20, 0 and discharging atoms in(all_27_1_10, all_0_5_5) = all_66_1_20, in(all_27_1_10, all_0_5_5) = 0, yields:
% 4.50/1.83  		| (53) all_66_1_20 = 0
% 4.50/1.83  		|
% 4.50/1.83  		| Instantiating formula (5) with all_27_1_10, all_0_6_6, all_60_1_16, 0 and discharging atoms in(all_27_1_10, all_0_6_6) = all_60_1_16, in(all_27_1_10, all_0_6_6) = 0, yields:
% 4.50/1.83  		| (54) all_60_1_16 = 0
% 4.50/1.83  		|
% 4.50/1.83  		| Using (45) and (51) yields:
% 4.50/1.83  		| (55)  ~ (all_60_1_16 = all_27_0_9)
% 4.50/1.83  		|
% 4.50/1.83  		| Equations (54) can reduce 55 to:
% 4.50/1.83  		| (56)  ~ (all_27_0_9 = 0)
% 4.50/1.83  		|
% 4.50/1.83  		| Simplifying 56 yields:
% 4.50/1.83  		| (35)  ~ (all_27_0_9 = 0)
% 4.50/1.83  		|
% 4.50/1.83  		+-Applying beta-rule and splitting (50), into two cases.
% 4.50/1.83  		|-Branch one:
% 4.50/1.83  		| (58)  ~ (all_66_1_20 = 0)
% 4.50/1.83  		|
% 4.50/1.83  			| Equations (53) can reduce 58 to:
% 4.50/1.83  			| (31) $false
% 4.50/1.83  			|
% 4.50/1.83  			|-The branch is then unsatisfiable
% 4.50/1.83  		|-Branch two:
% 4.50/1.83  		| (53) all_66_1_20 = 0
% 4.50/1.83  		| (61) all_66_0_19 = 0
% 4.50/1.83  		|
% 4.50/1.83  			| Combining equations (61,52) yields a new equation:
% 4.50/1.83  			| (62) all_27_0_9 = 0
% 4.50/1.83  			|
% 4.50/1.83  			| Equations (62) can reduce 35 to:
% 4.50/1.83  			| (31) $false
% 4.50/1.83  			|
% 4.50/1.83  			|-The branch is then unsatisfiable
% 4.50/1.83  	|-Branch two:
% 4.50/1.83  	| (64) in(all_27_1_10, all_0_6_6) = all_27_0_9
% 4.50/1.83  	| (62) all_27_0_9 = 0
% 4.50/1.83  	|
% 4.50/1.83  		| Equations (62) can reduce 35 to:
% 4.50/1.83  		| (31) $false
% 4.50/1.83  		|
% 4.50/1.83  		|-The branch is then unsatisfiable
% 4.50/1.83  % SZS output end Proof for theBenchmark
% 4.50/1.83  
% 4.50/1.83  1237ms
%------------------------------------------------------------------------------