TSTP Solution File: SET959+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET959+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n022.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 00:23:27 EDT 2022

% Result   : Theorem 18.36s 5.29s
% Output   : Proof 77.32s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET959+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 17:09:55 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.59          ____       _                          
% 0.19/0.59    ___  / __ \_____(_)___  ________  __________
% 0.19/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.59  
% 0.19/0.59  A Theorem Prover for First-Order Logic
% 0.19/0.59  (ePrincess v.1.0)
% 0.19/0.59  
% 0.19/0.59  (c) Philipp Rümmer, 2009-2015
% 0.19/0.59  (c) Peter Backeman, 2014-2015
% 0.19/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59  Bug reports to peter@backeman.se
% 0.19/0.59  
% 0.19/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59  
% 0.19/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.34/0.89  Prover 0: Preprocessing ...
% 1.67/1.03  Prover 0: Warning: ignoring some quantifiers
% 1.67/1.04  Prover 0: Constructing countermodel ...
% 3.18/1.49  Prover 0: gave up
% 3.18/1.49  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.35/1.51  Prover 1: Preprocessing ...
% 3.52/1.56  Prover 1: Warning: ignoring some quantifiers
% 3.52/1.56  Prover 1: Constructing countermodel ...
% 3.52/1.58  Prover 1: gave up
% 3.52/1.58  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.52/1.60  Prover 2: Preprocessing ...
% 3.87/1.65  Prover 2: Warning: ignoring some quantifiers
% 3.87/1.65  Prover 2: Constructing countermodel ...
% 3.87/1.68  Prover 2: gave up
% 3.87/1.68  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.16/1.69  Prover 3: Preprocessing ...
% 4.16/1.72  Prover 3: Warning: ignoring some quantifiers
% 4.16/1.72  Prover 3: Constructing countermodel ...
% 4.16/1.74  Prover 3: gave up
% 4.16/1.74  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 4.16/1.75  Prover 4: Preprocessing ...
% 4.55/1.80  Prover 4: Warning: ignoring some quantifiers
% 4.55/1.80  Prover 4: Constructing countermodel ...
% 9.27/2.97  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 9.64/2.99  Prover 5: Preprocessing ...
% 9.79/3.02  Prover 5: Warning: ignoring some quantifiers
% 9.79/3.02  Prover 5: Constructing countermodel ...
% 9.79/3.04  Prover 5: gave up
% 9.79/3.04  Prover 6: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 9.79/3.06  Prover 6: Preprocessing ...
% 9.79/3.09  Prover 6: Warning: ignoring some quantifiers
% 9.79/3.10  Prover 6: Constructing countermodel ...
% 10.21/3.12  Prover 6: gave up
% 10.21/3.12  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 10.21/3.13  Prover 7: Preprocessing ...
% 10.21/3.15  Prover 7: Proving ...
% 18.36/5.29  Prover 7: proved (2165ms)
% 18.36/5.29  Prover 4: stopped
% 18.36/5.29  
% 18.36/5.29  % SZS status Theorem for theBenchmark
% 18.36/5.29  
% 18.36/5.29  Generating proof ... found it (size 49)
% 77.32/53.63  
% 77.32/53.63  % SZS output start Proof for theBenchmark
% 77.32/53.63  Assumed formulas after preprocessing and simplification: 
% 77.32/53.63  | (0)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ empty(v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) &  ! [v0] :  ! [v1] : (v1 = v0 |  ? [v2] : (( ~ in(v2, v1) |  ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) &  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1)) &  ? [v0] :  ? [v1] : ( ~ (v1 = v0) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) |  ~ in(v4, v1) | in(v4, v0)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) |  ~ in(v4, v0) | in(v4, v1)) &  ! [v2] : ( ~ in(v2, v1) |  ? [v3] :  ? [v4] : ordered_pair(v3, v4) = v2) &  ! [v2] : ( ~ in(v2, v0) |  ? [v3] :  ? [v4] : ordered_pair(v3, v4) = v2)) &  ? [v0] :  ~ empty(v0) &  ? [v0] : empty(v0)
% 77.32/53.65  | Applying alpha-rule on (0) yields:
% 77.32/53.65  | (1)  ? [v0] : empty(v0)
% 77.32/53.65  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 77.32/53.65  | (3)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 77.32/53.65  | (4)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 77.32/53.65  | (5)  ? [v0] :  ? [v1] : ( ~ (v1 = v0) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) |  ~ in(v4, v1) | in(v4, v0)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) |  ~ in(v4, v0) | in(v4, v1)) &  ! [v2] : ( ~ in(v2, v1) |  ? [v3] :  ? [v4] : ordered_pair(v3, v4) = v2) &  ! [v2] : ( ~ in(v2, v0) |  ? [v3] :  ? [v4] : ordered_pair(v3, v4) = v2))
% 77.32/53.65  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ empty(v2))
% 77.32/53.65  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 77.32/53.66  | (8)  ? [v0] :  ~ empty(v0)
% 77.32/53.66  | (9)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 77.32/53.66  | (10)  ! [v0] :  ! [v1] : (v1 = v0 |  ? [v2] : (( ~ in(v2, v1) |  ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 77.32/53.66  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 77.32/53.66  |
% 77.32/53.66  | Instantiating (5) with all_3_0_1, all_3_1_2 yields:
% 77.32/53.66  | (12)  ~ (all_3_0_1 = all_3_1_2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ in(v2, all_3_0_1) | in(v2, all_3_1_2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ in(v2, all_3_1_2) | in(v2, all_3_0_1)) &  ! [v0] : ( ~ in(v0, all_3_0_1) |  ? [v1] :  ? [v2] : ordered_pair(v1, v2) = v0) &  ! [v0] : ( ~ in(v0, all_3_1_2) |  ? [v1] :  ? [v2] : ordered_pair(v1, v2) = v0)
% 77.32/53.66  |
% 77.32/53.66  | Applying alpha-rule on (12) yields:
% 77.32/53.66  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ in(v2, all_3_1_2) | in(v2, all_3_0_1))
% 77.32/53.66  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ~ in(v2, all_3_0_1) | in(v2, all_3_1_2))
% 77.32/53.66  | (15)  ~ (all_3_0_1 = all_3_1_2)
% 77.32/53.66  | (16)  ! [v0] : ( ~ in(v0, all_3_0_1) |  ? [v1] :  ? [v2] : ordered_pair(v1, v2) = v0)
% 77.32/53.66  | (17)  ! [v0] : ( ~ in(v0, all_3_1_2) |  ? [v1] :  ? [v2] : ordered_pair(v1, v2) = v0)
% 77.32/53.66  |
% 77.32/53.66  | Introducing new symbol ex_14_1_5 defined by:
% 77.32/53.66  | (18) ex_14_1_5 = all_3_1_2
% 77.32/53.66  |
% 77.32/53.66  | Introducing new symbol ex_14_0_4 defined by:
% 77.32/53.66  | (19) ex_14_0_4 = all_3_0_1
% 77.32/53.66  |
% 77.32/53.66  | Instantiating formula (10) with ex_14_0_4, ex_14_1_5 yields:
% 77.32/53.66  | (20) ex_14_0_4 = ex_14_1_5 |  ? [v0] : (( ~ in(v0, ex_14_0_4) |  ~ in(v0, ex_14_1_5)) & (in(v0, ex_14_0_4) | in(v0, ex_14_1_5)))
% 77.32/53.66  |
% 77.32/53.66  +-Applying beta-rule and splitting (20), into two cases.
% 77.32/53.66  |-Branch one:
% 77.32/53.66  | (21) ex_14_0_4 = ex_14_1_5
% 77.32/53.66  |
% 77.32/53.66  	| Combining equations (19,21) yields a new equation:
% 77.32/53.66  	| (22) ex_14_1_5 = all_3_0_1
% 77.32/53.66  	|
% 77.32/53.66  	| Combining equations (22,18) yields a new equation:
% 77.32/53.66  	| (23) all_3_0_1 = all_3_1_2
% 77.32/53.66  	|
% 77.32/53.66  	| Simplifying 23 yields:
% 77.32/53.66  	| (24) all_3_0_1 = all_3_1_2
% 77.32/53.66  	|
% 77.32/53.66  	| Equations (24) can reduce 15 to:
% 77.32/53.66  	| (25) $false
% 77.32/53.66  	|
% 77.32/53.66  	|-The branch is then unsatisfiable
% 77.32/53.66  |-Branch two:
% 77.32/53.66  | (26)  ? [v0] : (( ~ in(v0, ex_14_0_4) |  ~ in(v0, ex_14_1_5)) & (in(v0, ex_14_0_4) | in(v0, ex_14_1_5)))
% 77.32/53.66  |
% 77.32/53.66  	| Instantiating (26) with all_17_0_6 yields:
% 77.32/53.66  	| (27) ( ~ in(all_17_0_6, ex_14_0_4) |  ~ in(all_17_0_6, ex_14_1_5)) & (in(all_17_0_6, ex_14_0_4) | in(all_17_0_6, ex_14_1_5))
% 77.32/53.66  	|
% 77.32/53.66  	| Applying alpha-rule on (27) yields:
% 77.32/53.66  	| (28)  ~ in(all_17_0_6, ex_14_0_4) |  ~ in(all_17_0_6, ex_14_1_5)
% 77.32/53.66  	| (29) in(all_17_0_6, ex_14_0_4) | in(all_17_0_6, ex_14_1_5)
% 77.32/53.67  	|
% 77.32/53.67  	+-Applying beta-rule and splitting (28), into two cases.
% 77.32/53.67  	|-Branch one:
% 77.32/53.67  	| (30)  ~ in(all_17_0_6, ex_14_0_4)
% 77.32/53.67  	|
% 77.32/53.67  		+-Applying beta-rule and splitting (29), into two cases.
% 77.32/53.67  		|-Branch one:
% 77.32/53.67  		| (31) in(all_17_0_6, ex_14_0_4)
% 77.32/53.67  		|
% 77.32/53.67  			| Using (31) and (30) yields:
% 77.32/53.67  			| (32) $false
% 77.32/53.67  			|
% 77.32/53.67  			|-The branch is then unsatisfiable
% 77.32/53.67  		|-Branch two:
% 77.32/53.67  		| (33) in(all_17_0_6, ex_14_1_5)
% 77.32/53.67  		|
% 77.32/53.67  			| Instantiating formula (16) with all_17_0_6 yields:
% 77.32/53.67  			| (34)  ~ in(all_17_0_6, all_3_0_1) |  ? [v0] :  ? [v1] : ordered_pair(v0, v1) = all_17_0_6
% 77.32/53.67  			|
% 77.32/53.67  			| Instantiating formula (17) with all_17_0_6 yields:
% 77.32/53.67  			| (35)  ~ in(all_17_0_6, all_3_1_2) |  ? [v0] :  ? [v1] : ordered_pair(v0, v1) = all_17_0_6
% 77.32/53.67  			|
% 77.32/53.67  			+-Applying beta-rule and splitting (35), into two cases.
% 77.32/53.67  			|-Branch one:
% 77.32/53.67  			| (36)  ~ in(all_17_0_6, all_3_1_2)
% 77.32/53.67  			|
% 77.32/53.67  				| From (18) and (33) follows:
% 77.32/53.67  				| (37) in(all_17_0_6, all_3_1_2)
% 77.32/53.67  				|
% 77.32/53.67  				| Using (37) and (36) yields:
% 77.32/53.67  				| (32) $false
% 77.32/53.67  				|
% 77.32/53.67  				|-The branch is then unsatisfiable
% 77.32/53.67  			|-Branch two:
% 77.32/53.67  			| (37) in(all_17_0_6, all_3_1_2)
% 77.32/53.67  			| (40)  ? [v0] :  ? [v1] : ordered_pair(v0, v1) = all_17_0_6
% 77.32/53.67  			|
% 77.32/53.67  				| Instantiating (40) with all_35_0_26, all_35_1_27 yields:
% 77.32/53.67  				| (41) ordered_pair(all_35_1_27, all_35_0_26) = all_17_0_6
% 77.32/53.67  				|
% 77.32/53.67  				| Instantiating formula (13) with all_17_0_6, all_35_0_26, all_35_1_27 and discharging atoms ordered_pair(all_35_1_27, all_35_0_26) = all_17_0_6, yields:
% 77.32/53.67  				| (42)  ~ in(all_17_0_6, all_3_1_2) | in(all_17_0_6, all_3_0_1)
% 77.32/53.67  				|
% 77.32/53.67  				+-Applying beta-rule and splitting (34), into two cases.
% 77.32/53.67  				|-Branch one:
% 77.32/53.67  				| (43)  ~ in(all_17_0_6, all_3_0_1)
% 77.32/53.67  				|
% 77.32/53.67  					+-Applying beta-rule and splitting (42), into two cases.
% 77.32/53.67  					|-Branch one:
% 77.32/53.67  					| (36)  ~ in(all_17_0_6, all_3_1_2)
% 77.32/53.67  					|
% 77.32/53.67  						| Using (37) and (36) yields:
% 77.32/53.67  						| (32) $false
% 77.32/53.67  						|
% 77.32/53.67  						|-The branch is then unsatisfiable
% 77.32/53.67  					|-Branch two:
% 77.32/53.67  					| (46) in(all_17_0_6, all_3_0_1)
% 77.32/53.67  					|
% 77.32/53.67  						| Using (46) and (43) yields:
% 77.32/53.67  						| (32) $false
% 77.32/53.67  						|
% 77.32/53.67  						|-The branch is then unsatisfiable
% 77.32/53.67  				|-Branch two:
% 77.32/53.67  				| (46) in(all_17_0_6, all_3_0_1)
% 77.32/53.67  				| (40)  ? [v0] :  ? [v1] : ordered_pair(v0, v1) = all_17_0_6
% 77.32/53.67  				|
% 77.32/53.67  					| From (19) and (30) follows:
% 77.32/53.67  					| (43)  ~ in(all_17_0_6, all_3_0_1)
% 77.32/53.67  					|
% 77.32/53.67  					| Using (46) and (43) yields:
% 77.32/53.67  					| (32) $false
% 77.32/53.67  					|
% 77.32/53.67  					|-The branch is then unsatisfiable
% 77.32/53.67  	|-Branch two:
% 77.32/53.67  	| (31) in(all_17_0_6, ex_14_0_4)
% 77.32/53.67  	| (53)  ~ in(all_17_0_6, ex_14_1_5)
% 77.32/53.67  	|
% 77.32/53.67  		| Instantiating formula (16) with all_17_0_6 yields:
% 77.32/53.67  		| (34)  ~ in(all_17_0_6, all_3_0_1) |  ? [v0] :  ? [v1] : ordered_pair(v0, v1) = all_17_0_6
% 77.32/53.67  		|
% 77.32/53.67  		| Instantiating formula (17) with all_17_0_6 yields:
% 77.32/53.67  		| (35)  ~ in(all_17_0_6, all_3_1_2) |  ? [v0] :  ? [v1] : ordered_pair(v0, v1) = all_17_0_6
% 77.32/53.67  		|
% 77.32/53.67  		+-Applying beta-rule and splitting (35), into two cases.
% 77.32/53.67  		|-Branch one:
% 77.32/53.67  		| (36)  ~ in(all_17_0_6, all_3_1_2)
% 77.32/53.67  		|
% 77.32/53.67  			+-Applying beta-rule and splitting (34), into two cases.
% 77.32/53.67  			|-Branch one:
% 77.32/53.67  			| (43)  ~ in(all_17_0_6, all_3_0_1)
% 77.32/53.67  			|
% 77.32/53.67  				| From (19) and (31) follows:
% 77.32/53.67  				| (46) in(all_17_0_6, all_3_0_1)
% 77.32/53.67  				|
% 77.32/53.67  				| Using (46) and (43) yields:
% 77.32/53.67  				| (32) $false
% 77.32/53.67  				|
% 77.32/53.67  				|-The branch is then unsatisfiable
% 77.32/53.67  			|-Branch two:
% 77.32/53.67  			| (46) in(all_17_0_6, all_3_0_1)
% 77.32/53.67  			| (40)  ? [v0] :  ? [v1] : ordered_pair(v0, v1) = all_17_0_6
% 77.32/53.67  			|
% 77.32/53.67  				| Instantiating (40) with all_42_0_28, all_42_1_29 yields:
% 77.32/53.67  				| (62) ordered_pair(all_42_1_29, all_42_0_28) = all_17_0_6
% 77.32/53.67  				|
% 77.32/53.67  				| Instantiating formula (14) with all_17_0_6, all_42_0_28, all_42_1_29 and discharging atoms ordered_pair(all_42_1_29, all_42_0_28) = all_17_0_6,  ~ in(all_17_0_6, all_3_1_2), yields:
% 77.32/53.67  				| (43)  ~ in(all_17_0_6, all_3_0_1)
% 77.32/53.67  				|
% 77.32/53.67  				| Using (46) and (43) yields:
% 77.32/53.67  				| (32) $false
% 77.32/53.67  				|
% 77.32/53.67  				|-The branch is then unsatisfiable
% 77.32/53.67  		|-Branch two:
% 77.32/53.67  		| (37) in(all_17_0_6, all_3_1_2)
% 77.32/53.67  		| (40)  ? [v0] :  ? [v1] : ordered_pair(v0, v1) = all_17_0_6
% 77.32/53.67  		|
% 77.32/53.67  			| From (18) and (53) follows:
% 77.32/53.67  			| (36)  ~ in(all_17_0_6, all_3_1_2)
% 77.32/53.67  			|
% 77.32/53.67  			| Using (37) and (36) yields:
% 77.32/53.67  			| (32) $false
% 77.32/53.67  			|
% 77.32/53.67  			|-The branch is then unsatisfiable
% 77.32/53.67  % SZS output end Proof for theBenchmark
% 77.32/53.67  
% 77.32/53.67  53068ms
%------------------------------------------------------------------------------