TSTP Solution File: PUZ031+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : PUZ031+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n021.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 18:08:51 EDT 2022

% Result   : Theorem 2.53s 1.28s
% Output   : Proof 3.24s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : PUZ031+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sat May 28 23:04:42 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.45/0.60          ____       _                          
% 0.45/0.60    ___  / __ \_____(_)___  ________  __________
% 0.45/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.45/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.45/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.45/0.60  
% 0.45/0.60  A Theorem Prover for First-Order Logic
% 0.45/0.60  (ePrincess v.1.0)
% 0.45/0.60  
% 0.45/0.60  (c) Philipp Rümmer, 2009-2015
% 0.45/0.60  (c) Peter Backeman, 2014-2015
% 0.45/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.45/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.45/0.60  Bug reports to peter@backeman.se
% 0.45/0.60  
% 0.45/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.45/0.60  
% 0.45/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.51/0.96  Prover 0: Preprocessing ...
% 1.87/1.09  Prover 0: Constructing countermodel ...
% 2.53/1.28  Prover 0: proved (622ms)
% 2.53/1.28  
% 2.53/1.28  No countermodel exists, formula is valid
% 2.53/1.28  % SZS status Theorem for theBenchmark
% 2.53/1.28  
% 2.53/1.28  Generating proof ... found it (size 27)
% 3.24/1.48  
% 3.24/1.48  % SZS output start Proof for theBenchmark
% 3.24/1.48  Assumed formulas after preprocessing and simplification: 
% 3.24/1.48  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : (grain(v0) & snail(v1) & caterpillar(v2) & bird(v3) & fox(v4) & wolf(v5) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ much_smaller(v7, v6) |  ~ eats(v7, v8) |  ~ plant(v9) |  ~ plant(v8) |  ~ animal(v7) |  ~ animal(v6) | eats(v6, v9) | eats(v6, v7)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ eats(v7, v8) |  ~ eats(v6, v7) |  ~ grain(v8) |  ~ animal(v7) |  ~ animal(v6)) &  ! [v6] :  ! [v7] : ( ~ eats(v6, v7) |  ~ grain(v7) |  ~ wolf(v6)) &  ! [v6] :  ! [v7] : ( ~ eats(v6, v7) |  ~ snail(v7) |  ~ bird(v6)) &  ! [v6] :  ! [v7] : ( ~ eats(v6, v7) |  ~ fox(v7) |  ~ wolf(v6)) &  ! [v6] :  ! [v7] : ( ~ snail(v6) |  ~ bird(v7) | much_smaller(v6, v7)) &  ! [v6] :  ! [v7] : ( ~ caterpillar(v7) |  ~ bird(v6) | eats(v6, v7)) &  ! [v6] :  ! [v7] : ( ~ caterpillar(v6) |  ~ bird(v7) | much_smaller(v6, v7)) &  ! [v6] :  ! [v7] : ( ~ bird(v6) |  ~ fox(v7) | much_smaller(v6, v7)) &  ! [v6] :  ! [v7] : ( ~ fox(v6) |  ~ wolf(v7) | much_smaller(v6, v7)) &  ! [v6] : ( ~ grain(v6) | plant(v6)) &  ! [v6] : ( ~ snail(v6) | animal(v6)) &  ! [v6] : ( ~ snail(v6) |  ? [v7] : (eats(v6, v7) & plant(v7))) &  ! [v6] : ( ~ caterpillar(v6) | animal(v6)) &  ! [v6] : ( ~ caterpillar(v6) |  ? [v7] : (eats(v6, v7) & plant(v7))) &  ! [v6] : ( ~ bird(v6) | animal(v6)) &  ! [v6] : ( ~ fox(v6) | animal(v6)) &  ! [v6] : ( ~ wolf(v6) | animal(v6)))
% 3.24/1.49  | 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 yields:
% 3.24/1.49  | (1) grain(all_0_5_5) & snail(all_0_4_4) & caterpillar(all_0_3_3) & bird(all_0_2_2) & fox(all_0_1_1) & wolf(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(v0) |  ~ bird(v1) | much_smaller(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ caterpillar(v1) |  ~ bird(v0) | eats(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ caterpillar(v0) |  ~ bird(v1) | much_smaller(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] : ( ~ 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))
% 3.24/1.50  |
% 3.24/1.50  | Applying alpha-rule on (1) yields:
% 3.24/1.50  | (2) bird(all_0_2_2)
% 3.24/1.50  | (3) caterpillar(all_0_3_3)
% 3.24/1.50  | (4)  ! [v0] :  ! [v1] : ( ~ eats(v0, v1) |  ~ fox(v1) |  ~ wolf(v0))
% 3.24/1.50  | (5)  ! [v0] : ( ~ bird(v0) | animal(v0))
% 3.24/1.50  | (6) fox(all_0_1_1)
% 3.24/1.50  | (7)  ! [v0] : ( ~ fox(v0) | animal(v0))
% 3.24/1.50  | (8)  ! [v0] :  ! [v1] : ( ~ snail(v0) |  ~ bird(v1) | much_smaller(v0, v1))
% 3.24/1.51  | (9)  ! [v0] : ( ~ wolf(v0) | animal(v0))
% 3.24/1.51  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ eats(v1, v2) |  ~ eats(v0, v1) |  ~ grain(v2) |  ~ animal(v1) |  ~ animal(v0))
% 3.24/1.51  | (11)  ! [v0] :  ! [v1] : ( ~ eats(v0, v1) |  ~ grain(v1) |  ~ wolf(v0))
% 3.24/1.51  | (12)  ! [v0] : ( ~ grain(v0) | plant(v0))
% 3.24/1.51  | (13)  ! [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))
% 3.24/1.51  | (14)  ! [v0] :  ! [v1] : ( ~ bird(v0) |  ~ fox(v1) | much_smaller(v0, v1))
% 3.24/1.51  | (15)  ! [v0] :  ! [v1] : ( ~ caterpillar(v0) |  ~ bird(v1) | much_smaller(v0, v1))
% 3.24/1.51  | (16)  ! [v0] :  ! [v1] : ( ~ eats(v0, v1) |  ~ snail(v1) |  ~ bird(v0))
% 3.24/1.51  | (17)  ! [v0] : ( ~ caterpillar(v0) | animal(v0))
% 3.24/1.51  | (18) grain(all_0_5_5)
% 3.24/1.51  | (19)  ! [v0] : ( ~ snail(v0) |  ? [v1] : (eats(v0, v1) & plant(v1)))
% 3.24/1.51  | (20)  ! [v0] :  ! [v1] : ( ~ fox(v0) |  ~ wolf(v1) | much_smaller(v0, v1))
% 3.24/1.51  | (21) wolf(all_0_0_0)
% 3.24/1.51  | (22)  ! [v0] : ( ~ caterpillar(v0) |  ? [v1] : (eats(v0, v1) & plant(v1)))
% 3.24/1.51  | (23)  ! [v0] : ( ~ snail(v0) | animal(v0))
% 3.24/1.51  | (24)  ! [v0] :  ! [v1] : ( ~ caterpillar(v1) |  ~ bird(v0) | eats(v0, v1))
% 3.24/1.51  | (25) snail(all_0_4_4)
% 3.24/1.51  |
% 3.24/1.51  | Instantiating formula (12) with all_0_5_5 and discharging atoms grain(all_0_5_5), yields:
% 3.24/1.51  | (26) plant(all_0_5_5)
% 3.24/1.51  |
% 3.24/1.51  | Instantiating formula (23) with all_0_4_4 and discharging atoms snail(all_0_4_4), yields:
% 3.24/1.51  | (27) animal(all_0_4_4)
% 3.24/1.51  |
% 3.24/1.51  | Instantiating formula (19) with all_0_4_4 and discharging atoms snail(all_0_4_4), yields:
% 3.24/1.51  | (28)  ? [v0] : (eats(all_0_4_4, v0) & plant(v0))
% 3.24/1.51  |
% 3.24/1.51  | Instantiating formula (8) with all_0_2_2, all_0_4_4 and discharging atoms snail(all_0_4_4), bird(all_0_2_2), yields:
% 3.24/1.51  | (29) much_smaller(all_0_4_4, all_0_2_2)
% 3.24/1.51  |
% 3.24/1.51  | Instantiating formula (5) with all_0_2_2 and discharging atoms bird(all_0_2_2), yields:
% 3.24/1.51  | (30) animal(all_0_2_2)
% 3.24/1.51  |
% 3.24/1.51  | Instantiating formula (14) with all_0_1_1, all_0_2_2 and discharging atoms bird(all_0_2_2), fox(all_0_1_1), yields:
% 3.24/1.51  | (31) much_smaller(all_0_2_2, all_0_1_1)
% 3.24/1.51  |
% 3.24/1.51  | Instantiating formula (7) with all_0_1_1 and discharging atoms fox(all_0_1_1), yields:
% 3.24/1.51  | (32) animal(all_0_1_1)
% 3.24/1.51  |
% 3.24/1.51  | Instantiating formula (20) with all_0_0_0, all_0_1_1 and discharging atoms fox(all_0_1_1), wolf(all_0_0_0), yields:
% 3.24/1.51  | (33) much_smaller(all_0_1_1, all_0_0_0)
% 3.24/1.51  |
% 3.24/1.51  | Instantiating formula (9) with all_0_0_0 and discharging atoms wolf(all_0_0_0), yields:
% 3.24/1.51  | (34) animal(all_0_0_0)
% 3.24/1.51  |
% 3.24/1.51  | Instantiating (28) with all_11_0_7 yields:
% 3.24/1.51  | (35) eats(all_0_4_4, all_11_0_7) & plant(all_11_0_7)
% 3.24/1.51  |
% 3.24/1.51  | Applying alpha-rule on (35) yields:
% 3.24/1.51  | (36) eats(all_0_4_4, all_11_0_7)
% 3.24/1.51  | (37) plant(all_11_0_7)
% 3.24/1.52  |
% 3.24/1.52  | Instantiating formula (13) with all_0_5_5, all_11_0_7, all_0_4_4, all_0_2_2 and discharging atoms much_smaller(all_0_4_4, all_0_2_2), eats(all_0_4_4, all_11_0_7), plant(all_11_0_7), plant(all_0_5_5), animal(all_0_2_2), animal(all_0_4_4), yields:
% 3.24/1.52  | (38) eats(all_0_2_2, all_0_4_4) | eats(all_0_2_2, all_0_5_5)
% 3.24/1.52  |
% 3.24/1.52  +-Applying beta-rule and splitting (38), into two cases.
% 3.24/1.52  |-Branch one:
% 3.24/1.52  | (39) eats(all_0_2_2, all_0_4_4)
% 3.24/1.52  |
% 3.24/1.52  	| Instantiating formula (16) with all_0_4_4, all_0_2_2 and discharging atoms eats(all_0_2_2, all_0_4_4), snail(all_0_4_4), bird(all_0_2_2), yields:
% 3.24/1.52  	| (40) $false
% 3.24/1.52  	|
% 3.24/1.52  	|-The branch is then unsatisfiable
% 3.24/1.52  |-Branch two:
% 3.24/1.52  | (41)  ~ eats(all_0_2_2, all_0_4_4)
% 3.24/1.52  | (42) eats(all_0_2_2, all_0_5_5)
% 3.24/1.52  |
% 3.24/1.52  	| Instantiating formula (13) with all_0_5_5, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms much_smaller(all_0_2_2, all_0_1_1), eats(all_0_2_2, all_0_5_5), plant(all_0_5_5), animal(all_0_1_1), animal(all_0_2_2), yields:
% 3.24/1.52  	| (43) eats(all_0_1_1, all_0_2_2) | eats(all_0_1_1, all_0_5_5)
% 3.24/1.52  	|
% 3.24/1.52  	+-Applying beta-rule and splitting (43), into two cases.
% 3.24/1.52  	|-Branch one:
% 3.24/1.52  	| (44) eats(all_0_1_1, all_0_2_2)
% 3.24/1.52  	|
% 3.24/1.52  		| Instantiating formula (10) with all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms eats(all_0_1_1, all_0_2_2), eats(all_0_2_2, all_0_5_5), grain(all_0_5_5), animal(all_0_1_1), animal(all_0_2_2), yields:
% 3.24/1.52  		| (40) $false
% 3.24/1.52  		|
% 3.24/1.52  		|-The branch is then unsatisfiable
% 3.24/1.52  	|-Branch two:
% 3.24/1.52  	| (46)  ~ eats(all_0_1_1, all_0_2_2)
% 3.24/1.52  	| (47) eats(all_0_1_1, all_0_5_5)
% 3.24/1.52  	|
% 3.24/1.52  		| Instantiating formula (13) with all_0_5_5, all_0_5_5, all_0_1_1, all_0_0_0 and discharging atoms much_smaller(all_0_1_1, all_0_0_0), eats(all_0_1_1, all_0_5_5), plant(all_0_5_5), animal(all_0_0_0), animal(all_0_1_1), yields:
% 3.24/1.52  		| (48) eats(all_0_0_0, all_0_1_1) | eats(all_0_0_0, all_0_5_5)
% 3.24/1.52  		|
% 3.24/1.52  		+-Applying beta-rule and splitting (48), into two cases.
% 3.24/1.52  		|-Branch one:
% 3.24/1.52  		| (49) eats(all_0_0_0, all_0_1_1)
% 3.24/1.52  		|
% 3.24/1.52  			| Instantiating formula (4) with all_0_1_1, all_0_0_0 and discharging atoms eats(all_0_0_0, all_0_1_1), fox(all_0_1_1), wolf(all_0_0_0), yields:
% 3.24/1.52  			| (40) $false
% 3.24/1.52  			|
% 3.24/1.52  			|-The branch is then unsatisfiable
% 3.24/1.52  		|-Branch two:
% 3.24/1.52  		| (51)  ~ eats(all_0_0_0, all_0_1_1)
% 3.24/1.52  		| (52) eats(all_0_0_0, all_0_5_5)
% 3.24/1.52  		|
% 3.24/1.52  			| Instantiating formula (11) with all_0_5_5, all_0_0_0 and discharging atoms eats(all_0_0_0, all_0_5_5), grain(all_0_5_5), wolf(all_0_0_0), yields:
% 3.24/1.52  			| (40) $false
% 3.24/1.52  			|
% 3.24/1.52  			|-The branch is then unsatisfiable
% 3.24/1.52  % SZS output end Proof for theBenchmark
% 3.24/1.52  
% 3.24/1.52  910ms
%------------------------------------------------------------------------------