TSTP Solution File: PUZ060+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : PUZ060+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n020.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 : Mon Jul 18 18:08:54 EDT 2022

% Result   : Theorem 2.86s 1.35s
% Output   : Proof 3.49s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : PUZ060+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n020.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 May 29 01:02:24 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.59          ____       _                          
% 0.20/0.59    ___  / __ \_____(_)___  ________  __________
% 0.20/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.20/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.20/0.59  
% 0.20/0.59  A Theorem Prover for First-Order Logic
% 0.20/0.59  (ePrincess v.1.0)
% 0.20/0.59  
% 0.20/0.59  (c) Philipp Rümmer, 2009-2015
% 0.20/0.59  (c) Peter Backeman, 2014-2015
% 0.20/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.59  Bug reports to peter@backeman.se
% 0.20/0.59  
% 0.20/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.59  
% 0.20/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.76/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.35/0.87  Prover 0: Preprocessing ...
% 1.43/0.93  Prover 0: Warning: ignoring some quantifiers
% 1.52/0.95  Prover 0: Constructing countermodel ...
% 1.93/1.07  Prover 0: gave up
% 1.93/1.07  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.93/1.09  Prover 1: Preprocessing ...
% 1.93/1.16  Prover 1: Constructing countermodel ...
% 2.41/1.23  Prover 1: gave up
% 2.41/1.23  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.41/1.24  Prover 2: Preprocessing ...
% 2.56/1.29  Prover 2: Warning: ignoring some quantifiers
% 2.56/1.30  Prover 2: Constructing countermodel ...
% 2.86/1.35  Prover 2: proved (125ms)
% 2.86/1.35  
% 2.86/1.35  No countermodel exists, formula is valid
% 2.86/1.35  % SZS status Theorem for theBenchmark
% 2.86/1.35  
% 2.86/1.35  Generating proof ... Warning: ignoring some quantifiers
% 3.39/1.53  found it (size 22)
% 3.39/1.53  
% 3.39/1.53  % SZS output start Proof for theBenchmark
% 3.39/1.53  Assumed formulas after preprocessing and simplification: 
% 3.39/1.53  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v6 = 0) & alive(v2) = 0 & eats(v2, v0) = 0 & likes(v1, v0) = v6 & food(v5) = 0 & food(v4) = 0 &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (not_killed_by(v10, v9) = v8) |  ~ (not_killed_by(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (eats(v10, v9) = v8) |  ~ (eats(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (likes(v10, v9) = v8) |  ~ (likes(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (alive(v7) = 0) |  ~ (not_killed_by(v7, v8) = v9)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (alive(v9) = v8) |  ~ (alive(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (food(v9) = v8) |  ~ (food(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = 0 |  ~ (not_killed_by(v9, v7) = 0) |  ~ (food(v7) = v8) |  ? [v10] : ( ~ (v10 = 0) & eats(v9, v7) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = 0 |  ~ (eats(v9, v7) = 0) |  ~ (food(v7) = v8) |  ? [v10] : ( ~ (v10 = 0) & not_killed_by(v9, v7) = v10)) &  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (eats(v3, v7) = v8) |  ? [v9] : ( ~ (v9 = 0) & eats(v2, v7) = v9)) &  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (likes(v1, v7) = v8) |  ? [v9] : ( ~ (v9 = 0) & food(v7) = v9)) &  ! [v7] : ( ~ (eats(v2, v7) = 0) | eats(v3, v7) = 0) &  ! [v7] : ( ~ (food(v7) = 0) | likes(v1, v7) = 0) &  ? [v7] :  ? [v8] :  ? [v9] : not_killed_by(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : eats(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : likes(v8, v7) = v9 &  ? [v7] :  ? [v8] : alive(v7) = v8 &  ? [v7] :  ? [v8] : food(v7) = v8)
% 3.49/1.56  | 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 yields:
% 3.49/1.56  | (1)  ~ (all_0_0_0 = 0) & alive(all_0_4_4) = 0 & eats(all_0_4_4, all_0_6_6) = 0 & likes(all_0_5_5, all_0_6_6) = all_0_0_0 & food(all_0_1_1) = 0 & food(all_0_2_2) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (not_killed_by(v3, v2) = v1) |  ~ (not_killed_by(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (eats(v3, v2) = v1) |  ~ (eats(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (likes(v3, v2) = v1) |  ~ (likes(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (alive(v0) = 0) |  ~ (not_killed_by(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (alive(v2) = v1) |  ~ (alive(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (food(v2) = v1) |  ~ (food(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = 0 |  ~ (not_killed_by(v2, v0) = 0) |  ~ (food(v0) = v1) |  ? [v3] : ( ~ (v3 = 0) & eats(v2, v0) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = 0 |  ~ (eats(v2, v0) = 0) |  ~ (food(v0) = v1) |  ? [v3] : ( ~ (v3 = 0) & not_killed_by(v2, v0) = v3)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (eats(all_0_3_3, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & eats(all_0_4_4, v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (likes(all_0_5_5, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & food(v0) = v2)) &  ! [v0] : ( ~ (eats(all_0_4_4, v0) = 0) | eats(all_0_3_3, v0) = 0) &  ! [v0] : ( ~ (food(v0) = 0) | likes(all_0_5_5, v0) = 0) &  ? [v0] :  ? [v1] :  ? [v2] : not_killed_by(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : eats(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : likes(v1, v0) = v2 &  ? [v0] :  ? [v1] : alive(v0) = v1 &  ? [v0] :  ? [v1] : food(v0) = v1
% 3.49/1.57  |
% 3.49/1.57  | Applying alpha-rule on (1) yields:
% 3.49/1.57  | (2)  ? [v0] :  ? [v1] :  ? [v2] : eats(v1, v0) = v2
% 3.49/1.57  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (likes(v3, v2) = v1) |  ~ (likes(v3, v2) = v0))
% 3.49/1.57  | (4)  ? [v0] :  ? [v1] :  ? [v2] : likes(v1, v0) = v2
% 3.49/1.57  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (not_killed_by(v3, v2) = v1) |  ~ (not_killed_by(v3, v2) = v0))
% 3.49/1.57  | (6)  ! [v0] : ( ~ (eats(all_0_4_4, v0) = 0) | eats(all_0_3_3, v0) = 0)
% 3.49/1.57  | (7) alive(all_0_4_4) = 0
% 3.49/1.57  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (alive(v0) = 0) |  ~ (not_killed_by(v0, v1) = v2))
% 3.49/1.57  | (9)  ~ (all_0_0_0 = 0)
% 3.49/1.57  | (10)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (alive(v2) = v1) |  ~ (alive(v2) = v0))
% 3.49/1.57  | (11)  ? [v0] :  ? [v1] :  ? [v2] : not_killed_by(v1, v0) = v2
% 3.49/1.57  | (12)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = 0 |  ~ (eats(v2, v0) = 0) |  ~ (food(v0) = v1) |  ? [v3] : ( ~ (v3 = 0) & not_killed_by(v2, v0) = v3))
% 3.49/1.57  | (13)  ! [v0] : ( ~ (food(v0) = 0) | likes(all_0_5_5, v0) = 0)
% 3.49/1.57  | (14) food(all_0_1_1) = 0
% 3.49/1.57  | (15)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = 0 |  ~ (not_killed_by(v2, v0) = 0) |  ~ (food(v0) = v1) |  ? [v3] : ( ~ (v3 = 0) & eats(v2, v0) = v3))
% 3.49/1.57  | (16) eats(all_0_4_4, all_0_6_6) = 0
% 3.49/1.57  | (17)  ? [v0] :  ? [v1] : alive(v0) = v1
% 3.49/1.57  | (18)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (eats(all_0_3_3, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & eats(all_0_4_4, v0) = v2))
% 3.49/1.57  | (19) likes(all_0_5_5, all_0_6_6) = all_0_0_0
% 3.49/1.57  | (20) food(all_0_2_2) = 0
% 3.49/1.57  | (21)  ? [v0] :  ? [v1] : food(v0) = v1
% 3.49/1.57  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (eats(v3, v2) = v1) |  ~ (eats(v3, v2) = v0))
% 3.49/1.57  | (23)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (likes(all_0_5_5, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & food(v0) = v2))
% 3.49/1.57  | (24)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (food(v2) = v1) |  ~ (food(v2) = v0))
% 3.49/1.57  |
% 3.49/1.57  | Instantiating formula (6) with all_0_6_6 and discharging atoms eats(all_0_4_4, all_0_6_6) = 0, yields:
% 3.49/1.57  | (25) eats(all_0_3_3, all_0_6_6) = 0
% 3.49/1.57  |
% 3.49/1.57  | Instantiating formula (23) with all_0_0_0, all_0_6_6 and discharging atoms likes(all_0_5_5, all_0_6_6) = all_0_0_0, yields:
% 3.49/1.57  | (26) all_0_0_0 = 0 |  ? [v0] : ( ~ (v0 = 0) & food(all_0_6_6) = v0)
% 3.49/1.57  |
% 3.49/1.57  +-Applying beta-rule and splitting (26), into two cases.
% 3.49/1.57  |-Branch one:
% 3.49/1.57  | (27) all_0_0_0 = 0
% 3.49/1.57  |
% 3.49/1.58  	| Equations (27) can reduce 9 to:
% 3.49/1.58  	| (28) $false
% 3.49/1.58  	|
% 3.49/1.58  	|-The branch is then unsatisfiable
% 3.49/1.58  |-Branch two:
% 3.49/1.58  | (9)  ~ (all_0_0_0 = 0)
% 3.49/1.58  | (30)  ? [v0] : ( ~ (v0 = 0) & food(all_0_6_6) = v0)
% 3.49/1.58  |
% 3.49/1.58  	| Instantiating (30) with all_23_0_20 yields:
% 3.49/1.58  	| (31)  ~ (all_23_0_20 = 0) & food(all_0_6_6) = all_23_0_20
% 3.49/1.58  	|
% 3.49/1.58  	| Applying alpha-rule on (31) yields:
% 3.49/1.58  	| (32)  ~ (all_23_0_20 = 0)
% 3.49/1.58  	| (33) food(all_0_6_6) = all_23_0_20
% 3.49/1.58  	|
% 3.49/1.58  	| Instantiating formula (12) with all_0_4_4, all_23_0_20, all_0_6_6 and discharging atoms eats(all_0_4_4, all_0_6_6) = 0, food(all_0_6_6) = all_23_0_20, yields:
% 3.49/1.58  	| (34) all_23_0_20 = 0 |  ? [v0] : ( ~ (v0 = 0) & not_killed_by(all_0_4_4, all_0_6_6) = v0)
% 3.49/1.58  	|
% 3.49/1.58  	| Instantiating formula (12) with all_0_3_3, all_23_0_20, all_0_6_6 and discharging atoms eats(all_0_3_3, all_0_6_6) = 0, food(all_0_6_6) = all_23_0_20, yields:
% 3.49/1.58  	| (35) all_23_0_20 = 0 |  ? [v0] : ( ~ (v0 = 0) & not_killed_by(all_0_3_3, all_0_6_6) = v0)
% 3.49/1.58  	|
% 3.49/1.58  	+-Applying beta-rule and splitting (35), into two cases.
% 3.49/1.58  	|-Branch one:
% 3.49/1.58  	| (36) all_23_0_20 = 0
% 3.49/1.58  	|
% 3.49/1.58  		| Equations (36) can reduce 32 to:
% 3.49/1.58  		| (28) $false
% 3.49/1.58  		|
% 3.49/1.58  		|-The branch is then unsatisfiable
% 3.49/1.58  	|-Branch two:
% 3.49/1.58  	| (32)  ~ (all_23_0_20 = 0)
% 3.49/1.58  	| (39)  ? [v0] : ( ~ (v0 = 0) & not_killed_by(all_0_3_3, all_0_6_6) = v0)
% 3.49/1.58  	|
% 3.49/1.58  		+-Applying beta-rule and splitting (34), into two cases.
% 3.49/1.58  		|-Branch one:
% 3.49/1.58  		| (36) all_23_0_20 = 0
% 3.49/1.58  		|
% 3.49/1.58  			| Equations (36) can reduce 32 to:
% 3.49/1.58  			| (28) $false
% 3.49/1.58  			|
% 3.49/1.58  			|-The branch is then unsatisfiable
% 3.49/1.58  		|-Branch two:
% 3.49/1.58  		| (32)  ~ (all_23_0_20 = 0)
% 3.49/1.58  		| (43)  ? [v0] : ( ~ (v0 = 0) & not_killed_by(all_0_4_4, all_0_6_6) = v0)
% 3.49/1.58  		|
% 3.49/1.58  			| Instantiating (43) with all_38_0_22 yields:
% 3.49/1.58  			| (44)  ~ (all_38_0_22 = 0) & not_killed_by(all_0_4_4, all_0_6_6) = all_38_0_22
% 3.49/1.58  			|
% 3.49/1.58  			| Applying alpha-rule on (44) yields:
% 3.49/1.58  			| (45)  ~ (all_38_0_22 = 0)
% 3.49/1.58  			| (46) not_killed_by(all_0_4_4, all_0_6_6) = all_38_0_22
% 3.49/1.58  			|
% 3.49/1.58  			| Instantiating formula (8) with all_38_0_22, all_0_6_6, all_0_4_4 and discharging atoms alive(all_0_4_4) = 0, not_killed_by(all_0_4_4, all_0_6_6) = all_38_0_22, yields:
% 3.49/1.58  			| (47) all_38_0_22 = 0
% 3.49/1.58  			|
% 3.49/1.58  			| Equations (47) can reduce 45 to:
% 3.49/1.58  			| (28) $false
% 3.49/1.58  			|
% 3.49/1.58  			|-The branch is then unsatisfiable
% 3.49/1.58  % SZS output end Proof for theBenchmark
% 3.49/1.58  
% 3.49/1.58  981ms
%------------------------------------------------------------------------------