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ePrincess---1.0.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KRS130+1 : TPTP v8.1.0. Released v3.1.0.
% 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 : Sun Jul 17 02:56:39 EDT 2022

% Result   : Theorem 2.21s 1.31s
% Output   : Proof 3.11s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12  % Problem  : KRS130+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.11/0.33  % Computer : n019.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Tue Jun  7 15:13:40 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.54/0.61          ____       _                          
% 0.54/0.61    ___  / __ \_____(_)___  ________  __________
% 0.54/0.61   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.61  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.54/0.61  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.54/0.61  
% 0.54/0.61  A Theorem Prover for First-Order Logic
% 0.54/0.62  (ePrincess v.1.0)
% 0.54/0.62  
% 0.54/0.62  (c) Philipp Rümmer, 2009-2015
% 0.54/0.62  (c) Peter Backeman, 2014-2015
% 0.54/0.62  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.62  Bug reports to peter@backeman.se
% 0.54/0.62  
% 0.54/0.62  For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.62  
% 0.54/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.69  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.36/0.97  Prover 0: Preprocessing ...
% 1.51/1.04  Prover 0: Warning: ignoring some quantifiers
% 1.51/1.05  Prover 0: Constructing countermodel ...
% 1.64/1.16  Prover 0: gave up
% 1.64/1.16  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.96/1.18  Prover 1: Preprocessing ...
% 2.21/1.25  Prover 1: Constructing countermodel ...
% 2.21/1.30  Prover 1: proved (144ms)
% 2.21/1.31  
% 2.21/1.31  No countermodel exists, formula is valid
% 2.21/1.31  % SZS status Theorem for theBenchmark
% 2.21/1.31  
% 2.21/1.31  Generating proof ... found it (size 54)
% 2.72/1.45  
% 2.72/1.45  % SZS output start Proof for theBenchmark
% 2.72/1.45  Assumed formulas after preprocessing and simplification: 
% 2.72/1.45  | (0)  ? [v0] :  ? [v1] :  ? [v2] : ( ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (rp(v6, v5) = v4) |  ~ (rp(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (cNothing(v5) = v4) |  ~ (cNothing(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (xsd_string(v5) = v4) |  ~ (xsd_string(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (xsd_integer(v5) = v4) |  ~ (xsd_integer(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (cowlNothing(v5) = v4) |  ~ (cowlNothing(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (cowlThing(v5) = v4) |  ~ (cowlThing(v5) = v3)) &  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (xsd_string(v3) = v4) | xsd_integer(v3) = 0) &  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (cowlThing(v3) = v4)) &  ! [v3] :  ! [v4] : ( ~ (cNothing(v3) = 0) |  ~ (rp(v3, v4) = 0)) &  ! [v3] : ( ~ (cNothing(v3) = 0) |  ? [v4] : rp(v3, v4) = 0) &  ! [v3] : ( ~ (xsd_string(v3) = 0) |  ? [v4] : ( ~ (v4 = 0) & xsd_integer(v3) = v4)) &  ! [v3] :  ~ (cowlNothing(v3) = 0) & ((cNothing(v0) = v1 & cowlNothing(v0) = v2 & ((v2 = 0 &  ~ (v1 = 0)) | (v1 = 0 &  ~ (v2 = 0)))) | (xsd_string(v0) = v1 & xsd_integer(v0) = v2 & ((v2 = 0 & v1 = 0) | ( ~ (v2 = 0) &  ~ (v1 = 0)))) | (cowlNothing(v0) = v2 & cowlThing(v0) = v1 & ( ~ (v1 = 0) | v2 = 0))))
% 2.99/1.48  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 2.99/1.48  | (1)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (rp(v3, v2) = v1) |  ~ (rp(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (cNothing(v2) = v1) |  ~ (cNothing(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (xsd_string(v2) = v1) |  ~ (xsd_string(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (xsd_integer(v2) = v1) |  ~ (xsd_integer(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (cowlNothing(v2) = v1) |  ~ (cowlNothing(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (cowlThing(v2) = v1) |  ~ (cowlThing(v2) = v0)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (cowlThing(v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (cNothing(v0) = 0) |  ~ (rp(v0, v1) = 0)) &  ! [v0] : ( ~ (cNothing(v0) = 0) |  ? [v1] : rp(v0, v1) = 0) &  ! [v0] : ( ~ (xsd_string(v0) = 0) |  ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) &  ! [v0] :  ~ (cowlNothing(v0) = 0) & ((cNothing(all_0_2_2) = all_0_1_1 & cowlNothing(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 &  ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 &  ~ (all_0_0_0 = 0)))) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) &  ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)))
% 2.99/1.48  |
% 2.99/1.48  | Applying alpha-rule on (1) yields:
% 2.99/1.48  | (2)  ! [v0] :  ! [v1] : ( ~ (cNothing(v0) = 0) |  ~ (rp(v0, v1) = 0))
% 2.99/1.48  | (3)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 2.99/1.48  | (4)  ! [v0] : ( ~ (cNothing(v0) = 0) |  ? [v1] : rp(v0, v1) = 0)
% 2.99/1.48  | (5)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (cowlThing(v2) = v1) |  ~ (cowlThing(v2) = v0))
% 2.99/1.48  | (6)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (xsd_string(v2) = v1) |  ~ (xsd_string(v2) = v0))
% 2.99/1.48  | (7)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (xsd_integer(v2) = v1) |  ~ (xsd_integer(v2) = v0))
% 2.99/1.48  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (cowlNothing(v2) = v1) |  ~ (cowlNothing(v2) = v0))
% 2.99/1.48  | (9)  ! [v0] :  ~ (cowlNothing(v0) = 0)
% 2.99/1.48  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (rp(v3, v2) = v1) |  ~ (rp(v3, v2) = v0))
% 2.99/1.48  | (11) (cNothing(all_0_2_2) = all_0_1_1 & cowlNothing(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 &  ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 &  ~ (all_0_0_0 = 0)))) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) &  ~ (all_0_1_1 = 0)))) | (cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))
% 2.99/1.49  | (12)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (cowlThing(v0) = v1))
% 2.99/1.49  | (13)  ! [v0] : ( ~ (xsd_string(v0) = 0) |  ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 2.99/1.49  | (14)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (cNothing(v2) = v1) |  ~ (cNothing(v2) = v0))
% 2.99/1.49  |
% 2.99/1.49  +-Applying beta-rule and splitting (11), into two cases.
% 2.99/1.49  |-Branch one:
% 2.99/1.49  | (15) (cNothing(all_0_2_2) = all_0_1_1 & cowlNothing(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 &  ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 &  ~ (all_0_0_0 = 0)))) | (xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) &  ~ (all_0_1_1 = 0))))
% 2.99/1.49  |
% 2.99/1.49  	+-Applying beta-rule and splitting (15), into two cases.
% 2.99/1.49  	|-Branch one:
% 2.99/1.49  	| (16) cNothing(all_0_2_2) = all_0_1_1 & cowlNothing(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 &  ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 &  ~ (all_0_0_0 = 0)))
% 2.99/1.49  	|
% 2.99/1.49  		| Applying alpha-rule on (16) yields:
% 2.99/1.49  		| (17) cNothing(all_0_2_2) = all_0_1_1
% 2.99/1.49  		| (18) cowlNothing(all_0_2_2) = all_0_0_0
% 2.99/1.49  		| (19) (all_0_0_0 = 0 &  ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 &  ~ (all_0_0_0 = 0))
% 2.99/1.49  		|
% 2.99/1.49  		| Instantiating formula (9) with all_0_2_2 yields:
% 2.99/1.49  		| (20)  ~ (cowlNothing(all_0_2_2) = 0)
% 2.99/1.49  		|
% 2.99/1.49  		| Using (18) and (20) yields:
% 2.99/1.49  		| (21)  ~ (all_0_0_0 = 0)
% 2.99/1.49  		|
% 2.99/1.49  		+-Applying beta-rule and splitting (19), into two cases.
% 2.99/1.49  		|-Branch one:
% 2.99/1.49  		| (22) all_0_0_0 = 0 &  ~ (all_0_1_1 = 0)
% 2.99/1.49  		|
% 2.99/1.49  			| Applying alpha-rule on (22) yields:
% 2.99/1.49  			| (23) all_0_0_0 = 0
% 2.99/1.49  			| (24)  ~ (all_0_1_1 = 0)
% 2.99/1.49  			|
% 2.99/1.49  			| Equations (23) can reduce 21 to:
% 2.99/1.49  			| (25) $false
% 2.99/1.49  			|
% 2.99/1.49  			|-The branch is then unsatisfiable
% 2.99/1.49  		|-Branch two:
% 2.99/1.49  		| (26) all_0_1_1 = 0 &  ~ (all_0_0_0 = 0)
% 2.99/1.49  		|
% 2.99/1.49  			| Applying alpha-rule on (26) yields:
% 2.99/1.49  			| (27) all_0_1_1 = 0
% 2.99/1.49  			| (21)  ~ (all_0_0_0 = 0)
% 2.99/1.49  			|
% 2.99/1.49  			| From (27) and (17) follows:
% 2.99/1.49  			| (29) cNothing(all_0_2_2) = 0
% 2.99/1.49  			|
% 2.99/1.49  			| Instantiating formula (4) with all_0_2_2 and discharging atoms cNothing(all_0_2_2) = 0, yields:
% 2.99/1.49  			| (30)  ? [v0] : rp(all_0_2_2, v0) = 0
% 2.99/1.49  			|
% 2.99/1.49  			| Instantiating (30) with all_23_0_3 yields:
% 2.99/1.49  			| (31) rp(all_0_2_2, all_23_0_3) = 0
% 2.99/1.49  			|
% 2.99/1.49  			| Instantiating formula (2) with all_23_0_3, all_0_2_2 and discharging atoms cNothing(all_0_2_2) = 0, rp(all_0_2_2, all_23_0_3) = 0, yields:
% 2.99/1.49  			| (32) $false
% 2.99/1.49  			|
% 2.99/1.49  			|-The branch is then unsatisfiable
% 2.99/1.49  	|-Branch two:
% 2.99/1.49  	| (33) xsd_string(all_0_2_2) = all_0_1_1 & xsd_integer(all_0_2_2) = all_0_0_0 & ((all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) &  ~ (all_0_1_1 = 0)))
% 2.99/1.49  	|
% 2.99/1.49  		| Applying alpha-rule on (33) yields:
% 2.99/1.49  		| (34) xsd_string(all_0_2_2) = all_0_1_1
% 2.99/1.49  		| (35) xsd_integer(all_0_2_2) = all_0_0_0
% 2.99/1.49  		| (36) (all_0_0_0 = 0 & all_0_1_1 = 0) | ( ~ (all_0_0_0 = 0) &  ~ (all_0_1_1 = 0))
% 2.99/1.49  		|
% 2.99/1.49  		| Instantiating formula (13) with all_0_2_2 yields:
% 2.99/1.49  		| (37)  ~ (xsd_string(all_0_2_2) = 0) |  ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 2.99/1.49  		|
% 2.99/1.49  		| Instantiating formula (3) with all_0_1_1, all_0_2_2 and discharging atoms xsd_string(all_0_2_2) = all_0_1_1, yields:
% 2.99/1.49  		| (38) all_0_1_1 = 0 | xsd_integer(all_0_2_2) = 0
% 2.99/1.49  		|
% 2.99/1.49  		+-Applying beta-rule and splitting (38), into two cases.
% 2.99/1.49  		|-Branch one:
% 2.99/1.49  		| (39) xsd_integer(all_0_2_2) = 0
% 2.99/1.49  		|
% 2.99/1.49  			| Instantiating formula (7) with all_0_2_2, 0, all_0_0_0 and discharging atoms xsd_integer(all_0_2_2) = all_0_0_0, xsd_integer(all_0_2_2) = 0, yields:
% 2.99/1.50  			| (23) all_0_0_0 = 0
% 2.99/1.50  			|
% 2.99/1.50  			| From (23) and (35) follows:
% 2.99/1.50  			| (39) xsd_integer(all_0_2_2) = 0
% 2.99/1.50  			|
% 2.99/1.50  			+-Applying beta-rule and splitting (37), into two cases.
% 2.99/1.50  			|-Branch one:
% 2.99/1.50  			| (42)  ~ (xsd_string(all_0_2_2) = 0)
% 2.99/1.50  			|
% 2.99/1.50  				+-Applying beta-rule and splitting (36), into two cases.
% 2.99/1.50  				|-Branch one:
% 2.99/1.50  				| (43) all_0_0_0 = 0 & all_0_1_1 = 0
% 2.99/1.50  				|
% 2.99/1.50  					| Applying alpha-rule on (43) yields:
% 2.99/1.50  					| (23) all_0_0_0 = 0
% 2.99/1.50  					| (27) all_0_1_1 = 0
% 2.99/1.50  					|
% 2.99/1.50  					| From (27) and (34) follows:
% 2.99/1.50  					| (46) xsd_string(all_0_2_2) = 0
% 2.99/1.50  					|
% 2.99/1.50  					| Using (46) and (42) yields:
% 2.99/1.50  					| (32) $false
% 2.99/1.50  					|
% 2.99/1.50  					|-The branch is then unsatisfiable
% 2.99/1.50  				|-Branch two:
% 2.99/1.50  				| (48)  ~ (all_0_0_0 = 0) &  ~ (all_0_1_1 = 0)
% 2.99/1.50  				|
% 2.99/1.50  					| Applying alpha-rule on (48) yields:
% 2.99/1.50  					| (21)  ~ (all_0_0_0 = 0)
% 2.99/1.50  					| (24)  ~ (all_0_1_1 = 0)
% 2.99/1.50  					|
% 2.99/1.50  					| Equations (23) can reduce 21 to:
% 2.99/1.50  					| (25) $false
% 2.99/1.50  					|
% 2.99/1.50  					|-The branch is then unsatisfiable
% 2.99/1.50  			|-Branch two:
% 2.99/1.50  			| (46) xsd_string(all_0_2_2) = 0
% 2.99/1.50  			| (53)  ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_2_2) = v0)
% 2.99/1.50  			|
% 2.99/1.50  				| Instantiating (53) with all_21_0_4 yields:
% 2.99/1.50  				| (54)  ~ (all_21_0_4 = 0) & xsd_integer(all_0_2_2) = all_21_0_4
% 3.11/1.50  				|
% 3.11/1.50  				| Applying alpha-rule on (54) yields:
% 3.11/1.50  				| (55)  ~ (all_21_0_4 = 0)
% 3.11/1.50  				| (56) xsd_integer(all_0_2_2) = all_21_0_4
% 3.11/1.50  				|
% 3.11/1.50  				| Instantiating formula (7) with all_0_2_2, all_21_0_4, 0 and discharging atoms xsd_integer(all_0_2_2) = all_21_0_4, xsd_integer(all_0_2_2) = 0, yields:
% 3.11/1.50  				| (57) all_21_0_4 = 0
% 3.11/1.50  				|
% 3.11/1.50  				| Equations (57) can reduce 55 to:
% 3.11/1.50  				| (25) $false
% 3.11/1.50  				|
% 3.11/1.50  				|-The branch is then unsatisfiable
% 3.11/1.50  		|-Branch two:
% 3.11/1.50  		| (59)  ~ (xsd_integer(all_0_2_2) = 0)
% 3.11/1.50  		| (27) all_0_1_1 = 0
% 3.11/1.50  		|
% 3.11/1.50  			+-Applying beta-rule and splitting (36), into two cases.
% 3.11/1.50  			|-Branch one:
% 3.11/1.50  			| (43) all_0_0_0 = 0 & all_0_1_1 = 0
% 3.11/1.50  			|
% 3.11/1.50  				| Applying alpha-rule on (43) yields:
% 3.11/1.50  				| (23) all_0_0_0 = 0
% 3.11/1.50  				| (27) all_0_1_1 = 0
% 3.11/1.50  				|
% 3.11/1.50  				| From (23) and (35) follows:
% 3.11/1.50  				| (39) xsd_integer(all_0_2_2) = 0
% 3.11/1.50  				|
% 3.11/1.50  				| Using (39) and (59) yields:
% 3.11/1.50  				| (32) $false
% 3.11/1.50  				|
% 3.11/1.50  				|-The branch is then unsatisfiable
% 3.11/1.50  			|-Branch two:
% 3.11/1.50  			| (48)  ~ (all_0_0_0 = 0) &  ~ (all_0_1_1 = 0)
% 3.11/1.50  			|
% 3.11/1.50  				| Applying alpha-rule on (48) yields:
% 3.11/1.50  				| (21)  ~ (all_0_0_0 = 0)
% 3.11/1.50  				| (24)  ~ (all_0_1_1 = 0)
% 3.11/1.50  				|
% 3.11/1.50  				| Equations (27) can reduce 24 to:
% 3.11/1.50  				| (25) $false
% 3.11/1.50  				|
% 3.11/1.50  				|-The branch is then unsatisfiable
% 3.11/1.50  |-Branch two:
% 3.11/1.50  | (70) cowlNothing(all_0_2_2) = all_0_0_0 & cowlThing(all_0_2_2) = all_0_1_1 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)
% 3.11/1.50  |
% 3.11/1.50  	| Applying alpha-rule on (70) yields:
% 3.11/1.50  	| (18) cowlNothing(all_0_2_2) = all_0_0_0
% 3.11/1.50  	| (72) cowlThing(all_0_2_2) = all_0_1_1
% 3.11/1.50  	| (73)  ~ (all_0_1_1 = 0) | all_0_0_0 = 0
% 3.11/1.50  	|
% 3.11/1.50  	| Instantiating formula (9) with all_0_2_2 yields:
% 3.11/1.50  	| (20)  ~ (cowlNothing(all_0_2_2) = 0)
% 3.11/1.50  	|
% 3.11/1.50  	| Instantiating formula (12) with all_0_1_1, all_0_2_2 and discharging atoms cowlThing(all_0_2_2) = all_0_1_1, yields:
% 3.11/1.50  	| (27) all_0_1_1 = 0
% 3.11/1.50  	|
% 3.11/1.50  	+-Applying beta-rule and splitting (73), into two cases.
% 3.11/1.50  	|-Branch one:
% 3.11/1.50  	| (24)  ~ (all_0_1_1 = 0)
% 3.11/1.50  	|
% 3.11/1.50  		| Equations (27) can reduce 24 to:
% 3.11/1.50  		| (25) $false
% 3.11/1.50  		|
% 3.11/1.50  		|-The branch is then unsatisfiable
% 3.11/1.50  	|-Branch two:
% 3.11/1.50  	| (27) all_0_1_1 = 0
% 3.11/1.50  	| (23) all_0_0_0 = 0
% 3.11/1.50  	|
% 3.11/1.50  		| From (23) and (18) follows:
% 3.11/1.50  		| (80) cowlNothing(all_0_2_2) = 0
% 3.11/1.50  		|
% 3.11/1.50  		| Using (80) and (20) yields:
% 3.11/1.50  		| (32) $false
% 3.11/1.50  		|
% 3.11/1.50  		|-The branch is then unsatisfiable
% 3.11/1.50  % SZS output end Proof for theBenchmark
% 3.11/1.50  
% 3.11/1.50  871ms
%------------------------------------------------------------------------------