TSTP Solution File: KRS134+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KRS134+1 : TPTP v8.1.0. Released v3.1.0.
% 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 : Sun Jul 17 02:56:39 EDT 2022

% Result   : Theorem 2.03s 1.17s
% Output   : Proof 2.96s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : KRS134+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.12  % 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 : Tue Jun  7 12:29:16 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.57          ____       _                          
% 0.19/0.57    ___  / __ \_____(_)___  ________  __________
% 0.19/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.57  
% 0.19/0.57  A Theorem Prover for First-Order Logic
% 0.19/0.57  (ePrincess v.1.0)
% 0.19/0.57  
% 0.19/0.57  (c) Philipp Rümmer, 2009-2015
% 0.19/0.57  (c) Peter Backeman, 2014-2015
% 0.19/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.57  Bug reports to peter@backeman.se
% 0.19/0.57  
% 0.19/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.57  
% 0.19/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.76/0.62  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.18/0.86  Prover 0: Preprocessing ...
% 1.45/0.92  Prover 0: Warning: ignoring some quantifiers
% 1.53/0.94  Prover 0: Constructing countermodel ...
% 1.72/1.02  Prover 0: gave up
% 1.72/1.02  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.72/1.04  Prover 1: Preprocessing ...
% 2.03/1.11  Prover 1: Constructing countermodel ...
% 2.03/1.17  Prover 1: proved (147ms)
% 2.03/1.17  
% 2.03/1.17  No countermodel exists, formula is valid
% 2.03/1.17  % SZS status Theorem for theBenchmark
% 2.03/1.17  
% 2.03/1.17  Generating proof ... found it (size 46)
% 2.80/1.37  
% 2.80/1.37  % SZS output start Proof for theBenchmark
% 2.80/1.37  Assumed formulas after preprocessing and simplification: 
% 2.80/1.37  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : ( ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (rprop(v8, v7) = v6) |  ~ (rprop(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (cA(v7) = v6) |  ~ (cA(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (xsd_string(v7) = v6) |  ~ (xsd_string(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (xsd_integer(v7) = v6) |  ~ (xsd_integer(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (cowlNothing(v7) = v6) |  ~ (cowlNothing(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (cowlThing(v7) = v6) |  ~ (cowlThing(v7) = v5)) &  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (xsd_string(v5) = v6) | xsd_integer(v5) = 0) &  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (cowlThing(v5) = v6)) &  ! [v5] :  ! [v6] : ( ~ (rprop(v5, v6) = 0) | cA(v6) = 0) &  ! [v5] : ( ~ (xsd_string(v5) = 0) |  ? [v6] : ( ~ (v6 = 0) & xsd_integer(v5) = v6)) &  ! [v5] :  ~ (cowlNothing(v5) = 0) & ((v3 = 0 & v1 = 0 &  ~ (v4 = 0) & rprop(v0, v2) = 0 & cA(v2) = v4 & cowlThing(v0) = 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))))
% 2.96/1.41  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 2.96/1.41  | (1)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (rprop(v3, v2) = v1) |  ~ (rprop(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (cA(v2) = v1) |  ~ (cA(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] : ( ~ (rprop(v0, v1) = 0) | cA(v1) = 0) &  ! [v0] : ( ~ (xsd_string(v0) = 0) |  ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1)) &  ! [v0] :  ~ (cowlNothing(v0) = 0) & ((all_0_1_1 = 0 & all_0_3_3 = 0 &  ~ (all_0_0_0 = 0) & rprop(all_0_4_4, all_0_2_2) = 0 & cA(all_0_2_2) = all_0_0_0 & cowlThing(all_0_4_4) = 0) | (xsd_string(all_0_4_4) = all_0_3_3 & xsd_integer(all_0_4_4) = all_0_2_2 & ((all_0_2_2 = 0 & all_0_3_3 = 0) | ( ~ (all_0_2_2 = 0) &  ~ (all_0_3_3 = 0)))) | (cowlNothing(all_0_4_4) = all_0_2_2 & cowlThing(all_0_4_4) = all_0_3_3 & ( ~ (all_0_3_3 = 0) | all_0_2_2 = 0)))
% 2.96/1.41  |
% 2.96/1.41  | Applying alpha-rule on (1) yields:
% 2.96/1.41  | (2)  ! [v0] :  ~ (cowlNothing(v0) = 0)
% 2.96/1.41  | (3)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (xsd_string(v2) = v1) |  ~ (xsd_string(v2) = v0))
% 2.96/1.42  | (4)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (xsd_string(v0) = v1) | xsd_integer(v0) = 0)
% 2.96/1.42  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (rprop(v3, v2) = v1) |  ~ (rprop(v3, v2) = v0))
% 2.96/1.42  | (6)  ! [v0] : ( ~ (xsd_string(v0) = 0) |  ? [v1] : ( ~ (v1 = 0) & xsd_integer(v0) = v1))
% 2.96/1.42  | (7)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (cA(v2) = v1) |  ~ (cA(v2) = v0))
% 2.96/1.42  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (cowlThing(v2) = v1) |  ~ (cowlThing(v2) = v0))
% 2.96/1.42  | (9)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (cowlNothing(v2) = v1) |  ~ (cowlNothing(v2) = v0))
% 2.96/1.42  | (10)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (cowlThing(v0) = v1))
% 2.96/1.42  | (11)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (xsd_integer(v2) = v1) |  ~ (xsd_integer(v2) = v0))
% 2.96/1.42  | (12)  ! [v0] :  ! [v1] : ( ~ (rprop(v0, v1) = 0) | cA(v1) = 0)
% 2.96/1.42  | (13) (all_0_1_1 = 0 & all_0_3_3 = 0 &  ~ (all_0_0_0 = 0) & rprop(all_0_4_4, all_0_2_2) = 0 & cA(all_0_2_2) = all_0_0_0 & cowlThing(all_0_4_4) = 0) | (xsd_string(all_0_4_4) = all_0_3_3 & xsd_integer(all_0_4_4) = all_0_2_2 & ((all_0_2_2 = 0 & all_0_3_3 = 0) | ( ~ (all_0_2_2 = 0) &  ~ (all_0_3_3 = 0)))) | (cowlNothing(all_0_4_4) = all_0_2_2 & cowlThing(all_0_4_4) = all_0_3_3 & ( ~ (all_0_3_3 = 0) | all_0_2_2 = 0))
% 2.96/1.42  |
% 2.96/1.42  +-Applying beta-rule and splitting (13), into two cases.
% 2.96/1.42  |-Branch one:
% 2.96/1.42  | (14) (all_0_1_1 = 0 & all_0_3_3 = 0 &  ~ (all_0_0_0 = 0) & rprop(all_0_4_4, all_0_2_2) = 0 & cA(all_0_2_2) = all_0_0_0 & cowlThing(all_0_4_4) = 0) | (xsd_string(all_0_4_4) = all_0_3_3 & xsd_integer(all_0_4_4) = all_0_2_2 & ((all_0_2_2 = 0 & all_0_3_3 = 0) | ( ~ (all_0_2_2 = 0) &  ~ (all_0_3_3 = 0))))
% 2.96/1.42  |
% 2.96/1.42  	+-Applying beta-rule and splitting (14), into two cases.
% 2.96/1.42  	|-Branch one:
% 2.96/1.42  	| (15) all_0_1_1 = 0 & all_0_3_3 = 0 &  ~ (all_0_0_0 = 0) & rprop(all_0_4_4, all_0_2_2) = 0 & cA(all_0_2_2) = all_0_0_0 & cowlThing(all_0_4_4) = 0
% 2.96/1.42  	|
% 2.96/1.42  		| Applying alpha-rule on (15) yields:
% 2.96/1.42  		| (16)  ~ (all_0_0_0 = 0)
% 2.96/1.42  		| (17) all_0_3_3 = 0
% 2.96/1.42  		| (18) rprop(all_0_4_4, all_0_2_2) = 0
% 2.96/1.42  		| (19) cA(all_0_2_2) = all_0_0_0
% 2.96/1.42  		| (20) all_0_1_1 = 0
% 2.96/1.42  		| (21) cowlThing(all_0_4_4) = 0
% 2.96/1.42  		|
% 2.96/1.42  		| Instantiating formula (12) with all_0_2_2, all_0_4_4 and discharging atoms rprop(all_0_4_4, all_0_2_2) = 0, yields:
% 2.96/1.42  		| (22) cA(all_0_2_2) = 0
% 2.96/1.42  		|
% 2.96/1.42  		| Instantiating formula (7) with all_0_2_2, 0, all_0_0_0 and discharging atoms cA(all_0_2_2) = all_0_0_0, cA(all_0_2_2) = 0, yields:
% 2.96/1.42  		| (23) all_0_0_0 = 0
% 2.96/1.42  		|
% 2.96/1.42  		| Equations (23) can reduce 16 to:
% 2.96/1.42  		| (24) $false
% 2.96/1.42  		|
% 2.96/1.43  		|-The branch is then unsatisfiable
% 2.96/1.43  	|-Branch two:
% 2.96/1.43  	| (25) xsd_string(all_0_4_4) = all_0_3_3 & xsd_integer(all_0_4_4) = all_0_2_2 & ((all_0_2_2 = 0 & all_0_3_3 = 0) | ( ~ (all_0_2_2 = 0) &  ~ (all_0_3_3 = 0)))
% 2.96/1.43  	|
% 2.96/1.43  		| Applying alpha-rule on (25) yields:
% 2.96/1.43  		| (26) xsd_string(all_0_4_4) = all_0_3_3
% 2.96/1.43  		| (27) xsd_integer(all_0_4_4) = all_0_2_2
% 2.96/1.43  		| (28) (all_0_2_2 = 0 & all_0_3_3 = 0) | ( ~ (all_0_2_2 = 0) &  ~ (all_0_3_3 = 0))
% 2.96/1.43  		|
% 2.96/1.43  		| Instantiating formula (6) with all_0_4_4 yields:
% 2.96/1.43  		| (29)  ~ (xsd_string(all_0_4_4) = 0) |  ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_4_4) = v0)
% 2.96/1.43  		|
% 2.96/1.43  		| Instantiating formula (4) with all_0_3_3, all_0_4_4 and discharging atoms xsd_string(all_0_4_4) = all_0_3_3, yields:
% 2.96/1.43  		| (30) all_0_3_3 = 0 | xsd_integer(all_0_4_4) = 0
% 2.96/1.43  		|
% 2.96/1.43  		+-Applying beta-rule and splitting (30), into two cases.
% 2.96/1.43  		|-Branch one:
% 2.96/1.43  		| (31) xsd_integer(all_0_4_4) = 0
% 2.96/1.43  		|
% 2.96/1.43  			| Instantiating formula (11) with all_0_4_4, 0, all_0_2_2 and discharging atoms xsd_integer(all_0_4_4) = all_0_2_2, xsd_integer(all_0_4_4) = 0, yields:
% 2.96/1.43  			| (32) all_0_2_2 = 0
% 2.96/1.43  			|
% 2.96/1.43  			| From (32) and (27) follows:
% 2.96/1.43  			| (31) xsd_integer(all_0_4_4) = 0
% 2.96/1.43  			|
% 2.96/1.43  			+-Applying beta-rule and splitting (29), into two cases.
% 2.96/1.43  			|-Branch one:
% 2.96/1.43  			| (34)  ~ (xsd_string(all_0_4_4) = 0)
% 2.96/1.43  			|
% 2.96/1.43  				+-Applying beta-rule and splitting (28), into two cases.
% 2.96/1.43  				|-Branch one:
% 2.96/1.43  				| (35) all_0_2_2 = 0 & all_0_3_3 = 0
% 2.96/1.43  				|
% 2.96/1.43  					| Applying alpha-rule on (35) yields:
% 2.96/1.43  					| (32) all_0_2_2 = 0
% 2.96/1.43  					| (17) all_0_3_3 = 0
% 2.96/1.43  					|
% 2.96/1.43  					| From (17) and (26) follows:
% 2.96/1.43  					| (38) xsd_string(all_0_4_4) = 0
% 2.96/1.43  					|
% 2.96/1.43  					| Using (38) and (34) yields:
% 2.96/1.43  					| (39) $false
% 2.96/1.43  					|
% 2.96/1.43  					|-The branch is then unsatisfiable
% 2.96/1.43  				|-Branch two:
% 2.96/1.43  				| (40)  ~ (all_0_2_2 = 0) &  ~ (all_0_3_3 = 0)
% 2.96/1.43  				|
% 2.96/1.43  					| Applying alpha-rule on (40) yields:
% 2.96/1.43  					| (41)  ~ (all_0_2_2 = 0)
% 2.96/1.43  					| (42)  ~ (all_0_3_3 = 0)
% 2.96/1.43  					|
% 2.96/1.43  					| Equations (32) can reduce 41 to:
% 2.96/1.43  					| (24) $false
% 2.96/1.43  					|
% 2.96/1.43  					|-The branch is then unsatisfiable
% 2.96/1.43  			|-Branch two:
% 2.96/1.43  			| (38) xsd_string(all_0_4_4) = 0
% 2.96/1.43  			| (45)  ? [v0] : ( ~ (v0 = 0) & xsd_integer(all_0_4_4) = v0)
% 2.96/1.43  			|
% 2.96/1.43  				| Instantiating (45) with all_21_0_5 yields:
% 2.96/1.43  				| (46)  ~ (all_21_0_5 = 0) & xsd_integer(all_0_4_4) = all_21_0_5
% 2.96/1.43  				|
% 2.96/1.43  				| Applying alpha-rule on (46) yields:
% 2.96/1.43  				| (47)  ~ (all_21_0_5 = 0)
% 2.96/1.43  				| (48) xsd_integer(all_0_4_4) = all_21_0_5
% 2.96/1.43  				|
% 2.96/1.43  				| Instantiating formula (11) with all_0_4_4, all_21_0_5, 0 and discharging atoms xsd_integer(all_0_4_4) = all_21_0_5, xsd_integer(all_0_4_4) = 0, yields:
% 2.96/1.43  				| (49) all_21_0_5 = 0
% 2.96/1.43  				|
% 2.96/1.43  				| Equations (49) can reduce 47 to:
% 2.96/1.43  				| (24) $false
% 2.96/1.43  				|
% 2.96/1.43  				|-The branch is then unsatisfiable
% 2.96/1.43  		|-Branch two:
% 2.96/1.43  		| (51)  ~ (xsd_integer(all_0_4_4) = 0)
% 2.96/1.43  		| (17) all_0_3_3 = 0
% 2.96/1.43  		|
% 2.96/1.43  			+-Applying beta-rule and splitting (28), into two cases.
% 2.96/1.43  			|-Branch one:
% 2.96/1.43  			| (35) all_0_2_2 = 0 & all_0_3_3 = 0
% 2.96/1.43  			|
% 2.96/1.43  				| Applying alpha-rule on (35) yields:
% 2.96/1.43  				| (32) all_0_2_2 = 0
% 2.96/1.43  				| (17) all_0_3_3 = 0
% 2.96/1.43  				|
% 2.96/1.43  				| From (32) and (27) follows:
% 2.96/1.43  				| (31) xsd_integer(all_0_4_4) = 0
% 2.96/1.43  				|
% 2.96/1.43  				| Using (31) and (51) yields:
% 2.96/1.43  				| (39) $false
% 2.96/1.43  				|
% 2.96/1.43  				|-The branch is then unsatisfiable
% 2.96/1.43  			|-Branch two:
% 2.96/1.43  			| (40)  ~ (all_0_2_2 = 0) &  ~ (all_0_3_3 = 0)
% 2.96/1.43  			|
% 2.96/1.43  				| Applying alpha-rule on (40) yields:
% 2.96/1.43  				| (41)  ~ (all_0_2_2 = 0)
% 2.96/1.44  				| (42)  ~ (all_0_3_3 = 0)
% 2.96/1.44  				|
% 2.96/1.44  				| Equations (17) can reduce 42 to:
% 2.96/1.44  				| (24) $false
% 2.96/1.44  				|
% 2.96/1.44  				|-The branch is then unsatisfiable
% 2.96/1.44  |-Branch two:
% 2.96/1.44  | (62) cowlNothing(all_0_4_4) = all_0_2_2 & cowlThing(all_0_4_4) = all_0_3_3 & ( ~ (all_0_3_3 = 0) | all_0_2_2 = 0)
% 2.96/1.44  |
% 2.96/1.44  	| Applying alpha-rule on (62) yields:
% 2.96/1.44  	| (63) cowlNothing(all_0_4_4) = all_0_2_2
% 2.96/1.44  	| (64) cowlThing(all_0_4_4) = all_0_3_3
% 2.96/1.44  	| (65)  ~ (all_0_3_3 = 0) | all_0_2_2 = 0
% 2.96/1.44  	|
% 2.96/1.44  	| Instantiating formula (2) with all_0_4_4 yields:
% 2.96/1.44  	| (66)  ~ (cowlNothing(all_0_4_4) = 0)
% 2.96/1.44  	|
% 2.96/1.44  	| Instantiating formula (10) with all_0_3_3, all_0_4_4 and discharging atoms cowlThing(all_0_4_4) = all_0_3_3, yields:
% 2.96/1.44  	| (17) all_0_3_3 = 0
% 2.96/1.44  	|
% 2.96/1.44  	+-Applying beta-rule and splitting (65), into two cases.
% 2.96/1.44  	|-Branch one:
% 2.96/1.44  	| (42)  ~ (all_0_3_3 = 0)
% 2.96/1.44  	|
% 2.96/1.44  		| Equations (17) can reduce 42 to:
% 2.96/1.44  		| (24) $false
% 2.96/1.44  		|
% 2.96/1.44  		|-The branch is then unsatisfiable
% 2.96/1.44  	|-Branch two:
% 2.96/1.44  	| (17) all_0_3_3 = 0
% 2.96/1.44  	| (32) all_0_2_2 = 0
% 2.96/1.44  	|
% 2.96/1.44  		| From (32) and (63) follows:
% 2.96/1.44  		| (72) cowlNothing(all_0_4_4) = 0
% 2.96/1.44  		|
% 2.96/1.44  		| Using (72) and (66) yields:
% 2.96/1.44  		| (39) $false
% 2.96/1.44  		|
% 2.96/1.44  		|-The branch is then unsatisfiable
% 2.96/1.44  % SZS output end Proof for theBenchmark
% 2.96/1.44  
% 2.96/1.44  854ms
%------------------------------------------------------------------------------