%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ031-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:31:59 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.46s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 28
% Syntax : Number of formulae : 98 ( 22 unt; 8 def)
% Number of atoms : 301 ( 0 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 409 ( 206 ~; 195 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 110 ( 0 sgn 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ~ wolf(X0)
| animal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wolf_is_an_animal) ).
fof(f2,axiom,
! [X0] :
( ~ fox(X0)
| animal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fox_is_an_animal) ).
fof(f3,axiom,
! [X0] :
( ~ bird(X0)
| animal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bird_is_an_animal) ).
fof(f5,axiom,
! [X0] :
( ~ snail(X0)
| animal(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',snail_is_an_animal) ).
fof(f6,axiom,
wolf(a_wolf),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',there_is_a_wolf) ).
fof(f7,axiom,
fox(a_fox),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',there_is_a_fox) ).
fof(f8,axiom,
bird(a_bird),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',there_is_a_bird) ).
fof(f10,axiom,
snail(a_snail),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',there_is_a_snail) ).
fof(f11,axiom,
grain(a_grain),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',there_is_a_grain) ).
fof(f12,axiom,
! [X0] :
( ~ grain(X0)
| plant(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',grain_is_a_plant) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( ~ much_smaller(X2,X0)
| eats(X0,X2)
| ~ animal(X0)
| ~ plant(X1)
| ~ animal(X2)
| ~ plant(X3)
| eats(X0,X1)
| ~ eats(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eating_habits) ).
fof(f15,axiom,
! [X0,X1] :
( much_smaller(X0,X1)
| ~ snail(X0)
| ~ bird(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',snail_smaller_than_bird) ).
fof(f16,axiom,
! [X0,X1] :
( much_smaller(X0,X1)
| ~ bird(X0)
| ~ fox(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bird_smaller_than_fox) ).
fof(f17,axiom,
! [X0,X1] :
( much_smaller(X0,X1)
| ~ fox(X0)
| ~ wolf(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fox_smaller_than_wolf) ).
fof(f18,axiom,
! [X0,X1] :
( ~ fox(X1)
| ~ wolf(X0)
| ~ eats(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wolf_dont_eat_fox) ).
fof(f19,axiom,
! [X0,X1] :
( ~ grain(X1)
| ~ wolf(X0)
| ~ eats(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wolf_dont_eat_grain) ).
fof(f21,axiom,
! [X0,X1] :
( ~ snail(X1)
| ~ bird(X0)
| ~ eats(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bird_dont_eat_snail) ).
fof(f24,axiom,
! [X0] :
( plant(snail_food_of(X0))
| ~ snail(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',snail_food_is_a_plant) ).
fof(f25,axiom,
! [X0] :
( ~ snail(X0)
| eats(X0,snail_food_of(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',snail_eats_snail_food) ).
fof(f26,negated_conjecture,
! [X2,X0,X1] :
( ~ grain(X2)
| ~ animal(X1)
| ~ animal(X0)
| ~ eats(X0,X1)
| ~ eats(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_the_animal_exists) ).
fof(f27,plain,
! [X0,X1] :
( ~ animal(X0)
| ~ animal(X1)
| ~ eats(X1,X0)
| ~ eats(X0,a_grain) ),
inference(resolution,[],[f11,f26]) ).
fof(f29,plain,
animal(a_fox),
inference(resolution,[],[f2,f7]) ).
fof(f40,plain,
animal(a_bird),
inference(resolution,[],[f3,f8]) ).
fof(f45,plain,
! [X0] :
( ~ animal(X0)
| ~ eats(a_fox,X0)
| ~ eats(X0,a_grain) ),
inference(resolution,[],[f29,f27]) ).
fof(f60,plain,
plant(a_grain),
inference(resolution,[],[f12,f11]) ).
fof(f63,plain,
( ~ eats(a_fox,a_bird)
| ~ eats(a_bird,a_grain) ),
inference(resolution,[],[f40,f45]) ).
fof(f68,definition,
( spl0_6
<=> eats(a_bird,a_grain) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f70,plain,
( ~ eats(a_bird,a_grain)
| spl0_6 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f81,definition,
( spl0_9
<=> eats(a_fox,a_bird) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f83,plain,
( ~ eats(a_fox,a_bird)
| spl0_9 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,plain,
( ~ spl0_6
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f63,f81,f68]) ).
fof(f86,plain,
eats(a_snail,snail_food_of(a_snail)),
inference(resolution,[],[f25,f10]) ).
fof(f157,plain,
! [X0] :
( ~ wolf(X0)
| ~ eats(X0,a_grain) ),
inference(resolution,[],[f19,f11]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( eats(X0,X1)
| ~ animal(X0)
| ~ plant(X2)
| ~ animal(X1)
| ~ plant(X3)
| eats(X0,X2)
| ~ eats(X1,X3)
| ~ fox(X1)
| ~ wolf(X0) ),
inference(resolution,[],[f13,f17]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( eats(X0,X1)
| ~ animal(X0)
| ~ plant(X2)
| ~ animal(X1)
| ~ plant(X3)
| eats(X0,X2)
| ~ eats(X1,X3)
| ~ bird(X1)
| ~ fox(X0) ),
inference(resolution,[],[f13,f16]) ).
fof(f167,plain,
! [X2,X3,X0,X1] :
( eats(X0,X1)
| ~ animal(X0)
| ~ plant(X2)
| ~ animal(X1)
| ~ plant(X3)
| eats(X0,X2)
| ~ eats(X1,X3)
| ~ snail(X1)
| ~ bird(X0) ),
inference(resolution,[],[f13,f15]) ).
fof(f169,plain,
! [X2,X3,X0,X1] :
( ~ animal(X0)
| ~ plant(X2)
| ~ animal(X1)
| ~ plant(X3)
| eats(X0,X2)
| ~ eats(X1,X3)
| ~ snail(X1)
| ~ bird(X0) ),
inference(forward_subsumption_resolution,[],[f167,f21]) ).
fof(f170,plain,
! [X2,X3,X0,X1] :
( eats(X0,X1)
| ~ animal(X0)
| ~ plant(X2)
| ~ plant(X3)
| eats(X0,X2)
| ~ eats(X1,X3)
| ~ bird(X1)
| ~ fox(X0) ),
inference(forward_subsumption_resolution,[],[f166,f3]) ).
fof(f171,plain,
! [X2,X3,X0,X1] :
( ~ animal(X0)
| ~ plant(X2)
| ~ animal(X1)
| ~ plant(X3)
| eats(X0,X2)
| ~ eats(X1,X3)
| ~ fox(X1)
| ~ wolf(X0) ),
inference(forward_subsumption_resolution,[],[f165,f18]) ).
fof(f172,plain,
! [X2,X3,X0,X1] :
( ~ animal(X0)
| ~ plant(X2)
| ~ plant(X3)
| eats(X0,X2)
| ~ eats(X1,X3)
| ~ snail(X1)
| ~ bird(X0) ),
inference(forward_subsumption_resolution,[],[f169,f5]) ).
fof(f173,plain,
! [X2,X3,X0,X1] :
( ~ plant(X2)
| ~ plant(X3)
| eats(X0,X1)
| eats(X0,X2)
| ~ eats(X1,X3)
| ~ bird(X1)
| ~ fox(X0) ),
inference(forward_subsumption_resolution,[],[f170,f2]) ).
fof(f174,plain,
! [X2,X3,X0,X1] :
( ~ animal(X0)
| ~ plant(X2)
| ~ plant(X3)
| eats(X0,X2)
| ~ eats(X1,X3)
| ~ fox(X1)
| ~ wolf(X0) ),
inference(forward_subsumption_resolution,[],[f171,f2]) ).
fof(f175,plain,
! [X2,X3,X0,X1] :
( ~ plant(X2)
| ~ plant(X3)
| eats(X0,X2)
| ~ eats(X1,X3)
| ~ snail(X1)
| ~ bird(X0) ),
inference(forward_subsumption_resolution,[],[f172,f3]) ).
fof(f176,plain,
! [X2,X3,X0,X1] :
( ~ plant(X2)
| ~ plant(X3)
| eats(X0,X2)
| ~ eats(X1,X3)
| ~ fox(X1)
| ~ wolf(X0) ),
inference(forward_subsumption_resolution,[],[f174,f1]) ).
fof(f178,definition,
( spl0_21
<=> ! [X1,X3] :
( ~ plant(X3)
| ~ snail(X1)
| ~ eats(X1,X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f179,plain,
( ! [X3,X1] :
( ~ plant(X3)
| ~ snail(X1)
| ~ eats(X1,X3) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f181,definition,
( spl0_22
<=> ! [X2,X0] :
( ~ plant(X2)
| ~ bird(X0)
| eats(X0,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f182,plain,
( ! [X2,X0] :
( ~ plant(X2)
| ~ bird(X0)
| eats(X0,X2) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f183,plain,
( spl0_21
| spl0_22 ),
inference(avatar_split_clause,[],[f175,f181,f178]) ).
fof(f185,definition,
( spl0_23
<=> ! [X1,X3] :
( ~ plant(X3)
| ~ fox(X1)
| ~ eats(X1,X3) ) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f186,plain,
( ! [X3,X1] :
( ~ plant(X3)
| ~ fox(X1)
| ~ eats(X1,X3) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,definition,
( spl0_24
<=> ! [X2,X0] :
( ~ plant(X2)
| ~ wolf(X0)
| eats(X0,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
fof(f189,plain,
( ! [X2,X0] :
( ~ plant(X2)
| ~ wolf(X0)
| eats(X0,X2) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f190,plain,
( spl0_23
| spl0_24 ),
inference(avatar_split_clause,[],[f176,f188,f185]) ).
fof(f199,plain,
( ! [X0,X1] :
( ~ snail(X0)
| ~ snail(X1)
| ~ eats(X0,snail_food_of(X1)) )
| ~ spl0_21 ),
inference(resolution,[],[f179,f24]) ).
fof(f210,plain,
! [X2,X0,X1] :
( ~ plant(X0)
| eats(X1,X2)
| eats(X1,X0)
| ~ eats(X2,a_grain)
| ~ bird(X2)
| ~ fox(X1) ),
inference(resolution,[],[f173,f60]) ).
fof(f211,plain,
( ! [X2,X0,X1] :
( ~ plant(X0)
| eats(X1,X2)
| ~ eats(X2,a_grain)
| ~ bird(X2)
| ~ fox(X1) )
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f210,f186]) ).
fof(f218,definition,
( spl0_25
<=> ! [X2,X1] :
( eats(X1,X2)
| ~ fox(X1)
| ~ bird(X2)
| ~ eats(X2,a_grain) ) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f219,plain,
( ! [X2,X1] :
( ~ fox(X1)
| eats(X1,X2)
| ~ bird(X2)
| ~ eats(X2,a_grain) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f221,definition,
( spl0_26
<=> ! [X0] : ~ plant(X0) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f222,plain,
( ! [X0] : ~ plant(X0)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f223,plain,
( spl0_25
| spl0_26
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f211,f185,f221,f218]) ).
fof(f234,plain,
( ! [X0] :
( ~ wolf(X0)
| eats(X0,a_grain) )
| ~ spl0_24 ),
inference(resolution,[],[f189,f60]) ).
fof(f235,plain,
( ! [X0] : ~ wolf(X0)
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f234,f157]) ).
fof(f236,plain,
( $false
| ~ spl0_24 ),
inference(resolution,[],[f235,f6]) ).
fof(f237,plain,
~ spl0_24,
inference(avatar_contradiction_clause,[],[f236]) ).
fof(f240,plain,
( $false
| ~ spl0_26 ),
inference(resolution,[],[f222,f60]) ).
fof(f241,plain,
~ spl0_26,
inference(avatar_contradiction_clause,[],[f240]) ).
fof(f248,plain,
( ! [X0] :
( ~ snail(X0)
| ~ eats(a_snail,snail_food_of(X0)) )
| ~ spl0_21 ),
inference(resolution,[],[f199,f10]) ).
fof(f251,plain,
( ~ eats(a_snail,snail_food_of(a_snail))
| ~ spl0_21 ),
inference(resolution,[],[f248,f10]) ).
fof(f252,plain,
( $false
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f251,f86]) ).
fof(f253,plain,
~ spl0_21,
inference(avatar_contradiction_clause,[],[f252]) ).
fof(f256,plain,
( ! [X0] :
( ~ bird(X0)
| eats(X0,a_grain) )
| ~ spl0_22 ),
inference(resolution,[],[f182,f60]) ).
fof(f257,plain,
( eats(a_bird,a_grain)
| ~ spl0_22 ),
inference(resolution,[],[f256,f8]) ).
fof(f258,plain,
( $false
| spl0_6
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f257,f70]) ).
fof(f259,plain,
( spl0_6
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f258]) ).
fof(f271,plain,
( ! [X0] :
( eats(a_fox,X0)
| ~ bird(X0)
| ~ eats(X0,a_grain) )
| ~ spl0_25 ),
inference(resolution,[],[f219,f7]) ).
fof(f272,plain,
( ! [X0] :
( ~ bird(X0)
| eats(a_fox,X0) )
| ~ spl0_22
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f271,f256]) ).
fof(f273,plain,
( eats(a_fox,a_bird)
| ~ spl0_22
| ~ spl0_25 ),
inference(resolution,[],[f272,f8]) ).
fof(f274,plain,
( $false
| spl0_9
| ~ spl0_22
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[],[f273,f83]) ).
fof(f275,plain,
( spl0_9
| ~ spl0_22
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[],[f274]) ).
cnf(s6,plain,
( ~ spl0_6
| ~ spl0_9 ),
inference(sat_conversion,[],[f84]) ).
cnf(s16,plain,
( spl0_21
| spl0_22 ),
inference(sat_conversion,[],[f183]) ).
cnf(s17,plain,
( spl0_23
| spl0_24 ),
inference(sat_conversion,[],[f190]) ).
cnf(s21,plain,
( ~ spl0_23
| spl0_25
| spl0_26 ),
inference(sat_conversion,[],[f223]) ).
cnf(s24,plain,
~ spl0_24,
inference(sat_conversion,[],[f237]) ).
cnf(s25,plain,
~ spl0_26,
inference(sat_conversion,[],[f241]) ).
cnf(s26,plain,
~ spl0_21,
inference(sat_conversion,[],[f253]) ).
cnf(s27,plain,
( spl0_6
| ~ spl0_22 ),
inference(sat_conversion,[],[f259]) ).
cnf(s28,plain,
( spl0_9
| ~ spl0_22
| ~ spl0_25 ),
inference(sat_conversion,[],[f275]) ).
cnf(s31,plain,
( ~ spl0_23
| spl0_25 ),
inference(rat,[],[s21,s25]) ).
cnf(s32,plain,
spl0_23,
inference(rat,[],[s17,s24]) ).
cnf(s35,plain,
spl0_25,
inference(rat,[],[s31,s32]) ).
cnf(s36,plain,
spl0_22,
inference(rat,[],[s16,s26]) ).
cnf(s37,plain,
spl0_9,
inference(rat,[],[s28,s35,s36]) ).
cnf(s38,plain,
spl0_6,
inference(rat,[],[s27,s36]) ).
cnf(s40,plain,
$false,
inference(rat,[],[s6,s37,s38]) ).
fof(f276,plain,
$false,
inference(avatar_sat_refutation,[],[s40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ031-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n006.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 22:33:55 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.46 % (3390619)Will run a generic schedule for satisfiability detection.
% 0.13/0.46 % (3390628)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=913852936:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.13/0.46 % (3390628) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3390619-3390628"...
% 0.13/0.46 % (3390625)% WARNING: option uhcvi not known.
% 0.13/0.46 % (3390628)...printing done.
% 0.13/0.46 % (3390628)Refutation found. Thanks to Tanya!
% 0.13/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.46 % (3390628)------------------------------
% 0.13/0.46 % (3390628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.46 % (3390628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.46 % (3390628)CaDiCaL version: 2.1.3
% 0.13/0.46 % (3390628)Termination reason: Refutation
% 0.13/0.46 % (3390628)Time elapsed: 0.003 s
% 0.13/0.46 % (3390628)Peak memory usage: 12 MB
% 0.13/0.46 % (3390628)Instructions burned: 7 (million)
% 0.13/0.46 % (3390619)Success in time 0.029 s
% 0.13/0.46 % Vampire exiting
%------------------------------------------------------------------------------