TSTP Solution File: PUZ031+3 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : PUZ031+3 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n017.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 18:08:52 EDT 2022

% Result   : Theorem 2.66s 1.26s
% Output   : Proof 3.77s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : PUZ031+3 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n017.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 : Sat May 28 20:01:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.55/0.58          ____       _                          
% 0.55/0.58    ___  / __ \_____(_)___  ________  __________
% 0.55/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.55/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.55/0.58  
% 0.55/0.58  A Theorem Prover for First-Order Logic
% 0.55/0.58  (ePrincess v.1.0)
% 0.55/0.58  
% 0.55/0.58  (c) Philipp Rümmer, 2009-2015
% 0.55/0.58  (c) Peter Backeman, 2014-2015
% 0.55/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.58  Bug reports to peter@backeman.se
% 0.55/0.58  
% 0.55/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.58  
% 0.55/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.55/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.47/0.92  Prover 0: Preprocessing ...
% 1.88/1.05  Prover 0: Constructing countermodel ...
% 2.66/1.25  Prover 0: proved (627ms)
% 2.66/1.26  
% 2.66/1.26  No countermodel exists, formula is valid
% 2.66/1.26  % SZS status Theorem for theBenchmark
% 2.66/1.26  
% 2.66/1.26  Generating proof ... found it (size 31)
% 3.48/1.52  
% 3.48/1.52  % SZS output start Proof for theBenchmark
% 3.48/1.52  Assumed formulas after preprocessing and simplification: 
% 3.48/1.52  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : (grain(v0) & plant(v1) & snail(v2) & caterpillar(v3) & bird(v4) & fox(v5) & wolf(v6) & animal(v7) & edible(v8) &  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ much_smaller(v10, v9) |  ~ eats(v10, v11) |  ~ plant(v12) |  ~ plant(v11) |  ~ animal(v10) |  ~ animal(v9) | eats(v9, v12) | eats(v9, v10)) &  ! [v9] :  ! [v10] :  ! [v11] : ( ~ eats(v10, v11) |  ~ eats(v9, v10) |  ~ grain(v11) |  ~ animal(v10) |  ~ animal(v9)) &  ! [v9] :  ! [v10] : ( ~ eats(v9, v10) |  ~ grain(v10) |  ~ wolf(v9)) &  ! [v9] :  ! [v10] : ( ~ eats(v9, v10) |  ~ snail(v10) |  ~ bird(v9)) &  ! [v9] :  ! [v10] : ( ~ eats(v9, v10) |  ~ fox(v10) |  ~ wolf(v9)) &  ! [v9] :  ! [v10] : ( ~ snail(v10) |  ~ bird(v9) | much_smaller(v10, v9)) &  ! [v9] :  ! [v10] : ( ~ caterpillar(v10) |  ~ bird(v9) | much_smaller(v10, v9)) &  ! [v9] :  ! [v10] : ( ~ caterpillar(v10) |  ~ bird(v9) | eats(v9, v10)) &  ! [v9] :  ! [v10] : ( ~ bird(v9) |  ~ fox(v10) | much_smaller(v9, v10)) &  ! [v9] :  ! [v10] : ( ~ fox(v9) |  ~ wolf(v10) | much_smaller(v9, v10)) &  ! [v9] : ( ~ grain(v9) | plant(v9)) &  ! [v9] : ( ~ plant(v9) | edible(v9)) &  ! [v9] : ( ~ snail(v9) | animal(v9)) &  ! [v9] : ( ~ snail(v9) |  ? [v10] : (eats(v9, v10) & plant(v10))) &  ! [v9] : ( ~ caterpillar(v9) | animal(v9)) &  ! [v9] : ( ~ caterpillar(v9) |  ? [v10] : (eats(v9, v10) & plant(v10))) &  ! [v9] : ( ~ bird(v9) | animal(v9)) &  ! [v9] : ( ~ fox(v9) | animal(v9)) &  ! [v9] : ( ~ wolf(v9) | animal(v9)) &  ! [v9] : ( ~ animal(v9) | edible(v9)))
% 3.70/1.54  | 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, all_0_8_8 yields:
% 3.70/1.54  | (1) grain(all_0_8_8) & plant(all_0_7_7) & snail(all_0_6_6) & caterpillar(all_0_5_5) & bird(all_0_4_4) & fox(all_0_3_3) & wolf(all_0_2_2) & animal(all_0_1_1) & edible(all_0_0_0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ much_smaller(v1, v0) |  ~ eats(v1, v2) |  ~ plant(v3) |  ~ plant(v2) |  ~ animal(v1) |  ~ animal(v0) | eats(v0, v3) | eats(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ eats(v1, v2) |  ~ eats(v0, v1) |  ~ grain(v2) |  ~ animal(v1) |  ~ animal(v0)) &  ! [v0] :  ! [v1] : ( ~ eats(v0, v1) |  ~ grain(v1) |  ~ wolf(v0)) &  ! [v0] :  ! [v1] : ( ~ eats(v0, v1) |  ~ snail(v1) |  ~ bird(v0)) &  ! [v0] :  ! [v1] : ( ~ eats(v0, v1) |  ~ fox(v1) |  ~ wolf(v0)) &  ! [v0] :  ! [v1] : ( ~ snail(v1) |  ~ bird(v0) | much_smaller(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ caterpillar(v1) |  ~ bird(v0) | much_smaller(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ caterpillar(v1) |  ~ bird(v0) | eats(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ bird(v0) |  ~ fox(v1) | much_smaller(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ fox(v0) |  ~ wolf(v1) | much_smaller(v0, v1)) &  ! [v0] : ( ~ grain(v0) | plant(v0)) &  ! [v0] : ( ~ plant(v0) | edible(v0)) &  ! [v0] : ( ~ snail(v0) | animal(v0)) &  ! [v0] : ( ~ snail(v0) |  ? [v1] : (eats(v0, v1) & plant(v1))) &  ! [v0] : ( ~ caterpillar(v0) | animal(v0)) &  ! [v0] : ( ~ caterpillar(v0) |  ? [v1] : (eats(v0, v1) & plant(v1))) &  ! [v0] : ( ~ bird(v0) | animal(v0)) &  ! [v0] : ( ~ fox(v0) | animal(v0)) &  ! [v0] : ( ~ wolf(v0) | animal(v0)) &  ! [v0] : ( ~ animal(v0) | edible(v0))
% 3.70/1.54  |
% 3.70/1.54  | Applying alpha-rule on (1) yields:
% 3.70/1.54  | (2)  ! [v0] :  ! [v1] : ( ~ eats(v0, v1) |  ~ grain(v1) |  ~ wolf(v0))
% 3.70/1.54  | (3) animal(all_0_1_1)
% 3.70/1.54  | (4) caterpillar(all_0_5_5)
% 3.70/1.54  | (5)  ! [v0] : ( ~ wolf(v0) | animal(v0))
% 3.70/1.54  | (6) bird(all_0_4_4)
% 3.70/1.54  | (7)  ! [v0] : ( ~ animal(v0) | edible(v0))
% 3.70/1.54  | (8)  ! [v0] :  ! [v1] : ( ~ eats(v0, v1) |  ~ fox(v1) |  ~ wolf(v0))
% 3.70/1.55  | (9)  ! [v0] : ( ~ plant(v0) | edible(v0))
% 3.70/1.55  | (10)  ! [v0] :  ! [v1] : ( ~ caterpillar(v1) |  ~ bird(v0) | much_smaller(v1, v0))
% 3.70/1.55  | (11)  ! [v0] : ( ~ snail(v0) |  ? [v1] : (eats(v0, v1) & plant(v1)))
% 3.70/1.55  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ much_smaller(v1, v0) |  ~ eats(v1, v2) |  ~ plant(v3) |  ~ plant(v2) |  ~ animal(v1) |  ~ animal(v0) | eats(v0, v3) | eats(v0, v1))
% 3.70/1.55  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ eats(v1, v2) |  ~ eats(v0, v1) |  ~ grain(v2) |  ~ animal(v1) |  ~ animal(v0))
% 3.70/1.55  | (14)  ! [v0] : ( ~ snail(v0) | animal(v0))
% 3.70/1.55  | (15)  ! [v0] :  ! [v1] : ( ~ eats(v0, v1) |  ~ snail(v1) |  ~ bird(v0))
% 3.70/1.55  | (16)  ! [v0] :  ! [v1] : ( ~ caterpillar(v1) |  ~ bird(v0) | eats(v0, v1))
% 3.70/1.55  | (17) edible(all_0_0_0)
% 3.70/1.55  | (18) snail(all_0_6_6)
% 3.70/1.55  | (19) grain(all_0_8_8)
% 3.70/1.55  | (20) fox(all_0_3_3)
% 3.70/1.55  | (21)  ! [v0] : ( ~ bird(v0) | animal(v0))
% 3.70/1.55  | (22)  ! [v0] : ( ~ grain(v0) | plant(v0))
% 3.70/1.55  | (23)  ! [v0] :  ! [v1] : ( ~ bird(v0) |  ~ fox(v1) | much_smaller(v0, v1))
% 3.70/1.55  | (24)  ! [v0] : ( ~ caterpillar(v0) |  ? [v1] : (eats(v0, v1) & plant(v1)))
% 3.70/1.55  | (25) wolf(all_0_2_2)
% 3.70/1.55  | (26)  ! [v0] :  ! [v1] : ( ~ snail(v1) |  ~ bird(v0) | much_smaller(v1, v0))
% 3.70/1.55  | (27)  ! [v0] :  ! [v1] : ( ~ fox(v0) |  ~ wolf(v1) | much_smaller(v0, v1))
% 3.70/1.55  | (28) plant(all_0_7_7)
% 3.70/1.55  | (29)  ! [v0] : ( ~ caterpillar(v0) | animal(v0))
% 3.70/1.55  | (30)  ! [v0] : ( ~ fox(v0) | animal(v0))
% 3.70/1.55  |
% 3.70/1.55  | Instantiating formula (22) with all_0_8_8 and discharging atoms grain(all_0_8_8), yields:
% 3.77/1.55  | (31) plant(all_0_8_8)
% 3.77/1.55  |
% 3.77/1.55  | Instantiating formula (14) with all_0_6_6 and discharging atoms snail(all_0_6_6), yields:
% 3.77/1.55  | (32) animal(all_0_6_6)
% 3.77/1.55  |
% 3.77/1.55  | Instantiating formula (11) with all_0_6_6 and discharging atoms snail(all_0_6_6), yields:
% 3.77/1.55  | (33)  ? [v0] : (eats(all_0_6_6, v0) & plant(v0))
% 3.77/1.55  |
% 3.77/1.55  | Instantiating formula (26) with all_0_6_6, all_0_4_4 and discharging atoms snail(all_0_6_6), bird(all_0_4_4), yields:
% 3.77/1.55  | (34) much_smaller(all_0_6_6, all_0_4_4)
% 3.77/1.55  |
% 3.77/1.55  | Instantiating formula (21) with all_0_4_4 and discharging atoms bird(all_0_4_4), yields:
% 3.77/1.55  | (35) animal(all_0_4_4)
% 3.77/1.55  |
% 3.77/1.55  | Instantiating formula (23) with all_0_3_3, all_0_4_4 and discharging atoms bird(all_0_4_4), fox(all_0_3_3), yields:
% 3.77/1.55  | (36) much_smaller(all_0_4_4, all_0_3_3)
% 3.77/1.55  |
% 3.77/1.55  | Instantiating formula (30) with all_0_3_3 and discharging atoms fox(all_0_3_3), yields:
% 3.77/1.55  | (37) animal(all_0_3_3)
% 3.77/1.55  |
% 3.77/1.55  | Instantiating formula (27) with all_0_2_2, all_0_3_3 and discharging atoms fox(all_0_3_3), wolf(all_0_2_2), yields:
% 3.77/1.55  | (38) much_smaller(all_0_3_3, all_0_2_2)
% 3.77/1.55  |
% 3.77/1.55  | Instantiating formula (5) with all_0_2_2 and discharging atoms wolf(all_0_2_2), yields:
% 3.77/1.55  | (39) animal(all_0_2_2)
% 3.77/1.55  |
% 3.77/1.55  | Instantiating (33) with all_11_0_10 yields:
% 3.77/1.55  | (40) eats(all_0_6_6, all_11_0_10) & plant(all_11_0_10)
% 3.77/1.55  |
% 3.77/1.55  | Applying alpha-rule on (40) yields:
% 3.77/1.55  | (41) eats(all_0_6_6, all_11_0_10)
% 3.77/1.55  | (42) plant(all_11_0_10)
% 3.77/1.56  |
% 3.77/1.56  | Instantiating formula (12) with all_0_7_7, all_11_0_10, all_0_6_6, all_0_4_4 and discharging atoms much_smaller(all_0_6_6, all_0_4_4), eats(all_0_6_6, all_11_0_10), plant(all_11_0_10), plant(all_0_7_7), animal(all_0_4_4), animal(all_0_6_6), yields:
% 3.77/1.56  | (43) eats(all_0_4_4, all_0_6_6) | eats(all_0_4_4, all_0_7_7)
% 3.77/1.56  |
% 3.77/1.56  | Instantiating formula (12) with all_0_8_8, all_11_0_10, all_0_6_6, all_0_4_4 and discharging atoms much_smaller(all_0_6_6, all_0_4_4), eats(all_0_6_6, all_11_0_10), plant(all_11_0_10), plant(all_0_8_8), animal(all_0_4_4), animal(all_0_6_6), yields:
% 3.77/1.56  | (44) eats(all_0_4_4, all_0_6_6) | eats(all_0_4_4, all_0_8_8)
% 3.77/1.56  |
% 3.77/1.56  +-Applying beta-rule and splitting (43), into two cases.
% 3.77/1.56  |-Branch one:
% 3.77/1.56  | (45) eats(all_0_4_4, all_0_6_6)
% 3.77/1.56  |
% 3.77/1.56  	| Instantiating formula (15) with all_0_6_6, all_0_4_4 and discharging atoms eats(all_0_4_4, all_0_6_6), snail(all_0_6_6), bird(all_0_4_4), yields:
% 3.77/1.56  	| (46) $false
% 3.77/1.56  	|
% 3.77/1.56  	|-The branch is then unsatisfiable
% 3.77/1.56  |-Branch two:
% 3.77/1.56  | (47)  ~ eats(all_0_4_4, all_0_6_6)
% 3.77/1.56  | (48) eats(all_0_4_4, all_0_7_7)
% 3.77/1.56  |
% 3.77/1.56  	+-Applying beta-rule and splitting (44), into two cases.
% 3.77/1.56  	|-Branch one:
% 3.77/1.56  	| (45) eats(all_0_4_4, all_0_6_6)
% 3.77/1.56  	|
% 3.77/1.56  		| Using (45) and (47) yields:
% 3.77/1.56  		| (46) $false
% 3.77/1.56  		|
% 3.77/1.56  		|-The branch is then unsatisfiable
% 3.77/1.56  	|-Branch two:
% 3.77/1.56  	| (47)  ~ eats(all_0_4_4, all_0_6_6)
% 3.77/1.56  	| (52) eats(all_0_4_4, all_0_8_8)
% 3.77/1.56  	|
% 3.77/1.56  		| Instantiating formula (12) with all_0_8_8, all_0_8_8, all_0_4_4, all_0_3_3 and discharging atoms much_smaller(all_0_4_4, all_0_3_3), eats(all_0_4_4, all_0_8_8), plant(all_0_8_8), animal(all_0_3_3), animal(all_0_4_4), yields:
% 3.77/1.56  		| (53) eats(all_0_3_3, all_0_4_4) | eats(all_0_3_3, all_0_8_8)
% 3.77/1.56  		|
% 3.77/1.56  		+-Applying beta-rule and splitting (53), into two cases.
% 3.77/1.56  		|-Branch one:
% 3.77/1.56  		| (54) eats(all_0_3_3, all_0_4_4)
% 3.77/1.56  		|
% 3.77/1.56  			| Instantiating formula (13) with all_0_8_8, all_0_4_4, all_0_3_3 and discharging atoms eats(all_0_3_3, all_0_4_4), eats(all_0_4_4, all_0_8_8), grain(all_0_8_8), animal(all_0_3_3), animal(all_0_4_4), yields:
% 3.77/1.56  			| (46) $false
% 3.77/1.56  			|
% 3.77/1.56  			|-The branch is then unsatisfiable
% 3.77/1.56  		|-Branch two:
% 3.77/1.56  		| (56)  ~ eats(all_0_3_3, all_0_4_4)
% 3.77/1.56  		| (57) eats(all_0_3_3, all_0_8_8)
% 3.77/1.56  		|
% 3.77/1.56  			| Instantiating formula (12) with all_0_8_8, all_0_8_8, all_0_3_3, all_0_2_2 and discharging atoms much_smaller(all_0_3_3, all_0_2_2), eats(all_0_3_3, all_0_8_8), plant(all_0_8_8), animal(all_0_2_2), animal(all_0_3_3), yields:
% 3.77/1.56  			| (58) eats(all_0_2_2, all_0_3_3) | eats(all_0_2_2, all_0_8_8)
% 3.77/1.56  			|
% 3.77/1.56  			+-Applying beta-rule and splitting (58), into two cases.
% 3.77/1.56  			|-Branch one:
% 3.77/1.56  			| (59) eats(all_0_2_2, all_0_3_3)
% 3.77/1.56  			|
% 3.77/1.56  				| Instantiating formula (8) with all_0_3_3, all_0_2_2 and discharging atoms eats(all_0_2_2, all_0_3_3), fox(all_0_3_3), wolf(all_0_2_2), yields:
% 3.77/1.56  				| (46) $false
% 3.77/1.56  				|
% 3.77/1.56  				|-The branch is then unsatisfiable
% 3.77/1.56  			|-Branch two:
% 3.77/1.56  			| (61)  ~ eats(all_0_2_2, all_0_3_3)
% 3.77/1.56  			| (62) eats(all_0_2_2, all_0_8_8)
% 3.77/1.56  			|
% 3.77/1.56  				| Instantiating formula (2) with all_0_8_8, all_0_2_2 and discharging atoms eats(all_0_2_2, all_0_8_8), grain(all_0_8_8), wolf(all_0_2_2), yields:
% 3.77/1.56  				| (46) $false
% 3.77/1.56  				|
% 3.77/1.56  				|-The branch is then unsatisfiable
% 3.77/1.56  % SZS output end Proof for theBenchmark
% 3.77/1.57  
% 3.77/1.57  975ms
%------------------------------------------------------------------------------