%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ031-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 : Sun Sep 27 08:23:09 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 91 ( 29 unt; 0 def)
% Number of atoms : 241 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 311 ( 161 ~; 150 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 89 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(there_is_a_wolf,axiom,
wolf(a_wolf),
file('theBenchmark.p',there_is_a_wolf) ).
cnf(c_1,plain,
wolf(a_wolf),
inference(clausify,[status(thm)],[there_is_a_wolf]) ).
fof(wolf_is_an_animal,axiom,
! [VAR_0] :
( ~ wolf(VAR_0)
| animal(VAR_0) ),
file('theBenchmark.p',wolf_is_an_animal) ).
cnf(c_2,plain,
( ~ wolf(A)
| animal(A) ),
inference(clausify,[status(thm)],[wolf_is_an_animal]) ).
fof(fox_smaller_than_wolf,axiom,
! [VAR_0,VAR_1] :
( ~ wolf(VAR_1)
| ~ fox(VAR_0)
| much_smaller(VAR_0,VAR_1) ),
file('theBenchmark.p',fox_smaller_than_wolf) ).
cnf(c_3,plain,
( ~ wolf(B)
| ~ fox(A)
| much_smaller(A,B) ),
inference(clausify,[status(thm)],[fox_smaller_than_wolf]) ).
fof(wolf_dont_eat_fox,axiom,
! [VAR_0,VAR_1] :
( ~ eats(VAR_0,VAR_1)
| ~ fox(VAR_1)
| ~ wolf(VAR_0) ),
file('theBenchmark.p',wolf_dont_eat_fox) ).
cnf(c_4,plain,
( ~ eats(A,B)
| ~ fox(B)
| ~ wolf(A) ),
inference(clausify,[status(thm)],[wolf_dont_eat_fox]) ).
fof(wolf_dont_eat_grain,axiom,
! [VAR_0,VAR_1] :
( ~ eats(VAR_0,VAR_1)
| ~ grain(VAR_1)
| ~ wolf(VAR_0) ),
file('theBenchmark.p',wolf_dont_eat_grain) ).
cnf(c_5,plain,
( ~ eats(A,B)
| ~ grain(B)
| ~ wolf(A) ),
inference(clausify,[status(thm)],[wolf_dont_eat_grain]) ).
fof(there_is_a_fox,axiom,
fox(a_fox),
file('theBenchmark.p',there_is_a_fox) ).
cnf(c_6,plain,
fox(a_fox),
inference(clausify,[status(thm)],[there_is_a_fox]) ).
fof(bird_smaller_than_fox,axiom,
! [VAR_0,VAR_1] :
( ~ fox(VAR_1)
| ~ bird(VAR_0)
| much_smaller(VAR_0,VAR_1) ),
file('theBenchmark.p',bird_smaller_than_fox) ).
cnf(c_7,plain,
( ~ fox(B)
| ~ bird(A)
| much_smaller(A,B) ),
inference(clausify,[status(thm)],[bird_smaller_than_fox]) ).
cnf(c_8,plain,
( ~ fox(A)
| much_smaller(A,a_wolf) ),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_9,plain,
( ~ eats(a_wolf,A)
| ~ fox(A) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
fof(fox_is_an_animal,axiom,
! [VAR_0] :
( ~ fox(VAR_0)
| animal(VAR_0) ),
file('theBenchmark.p',fox_is_an_animal) ).
cnf(c_10,plain,
( ~ fox(A)
| animal(A) ),
inference(clausify,[status(thm)],[fox_is_an_animal]) ).
fof(there_is_a_bird,axiom,
bird(a_bird),
file('theBenchmark.p',there_is_a_bird) ).
cnf(c_11,plain,
bird(a_bird),
inference(clausify,[status(thm)],[there_is_a_bird]) ).
fof(bird_is_an_animal,axiom,
! [VAR_0] :
( ~ bird(VAR_0)
| animal(VAR_0) ),
file('theBenchmark.p',bird_is_an_animal) ).
cnf(c_12,plain,
( ~ bird(A)
| animal(A) ),
inference(clausify,[status(thm)],[bird_is_an_animal]) ).
cnf(c_13,plain,
( ~ bird(A)
| much_smaller(A,a_fox) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
fof(snail_smaller_than_bird,axiom,
! [VAR_0,VAR_1] :
( ~ bird(VAR_1)
| ~ snail(VAR_0)
| much_smaller(VAR_0,VAR_1) ),
file('theBenchmark.p',snail_smaller_than_bird) ).
cnf(c_15,plain,
( ~ bird(B)
| ~ snail(A)
| much_smaller(A,B) ),
inference(clausify,[status(thm)],[snail_smaller_than_bird]) ).
fof(bird_dont_eat_snail,axiom,
! [VAR_0,VAR_1] :
( ~ eats(VAR_0,VAR_1)
| ~ snail(VAR_1)
| ~ bird(VAR_0) ),
file('theBenchmark.p',bird_dont_eat_snail) ).
cnf(c_17,plain,
( ~ eats(A,B)
| ~ snail(B)
| ~ bird(A) ),
inference(clausify,[status(thm)],[bird_dont_eat_snail]) ).
fof(there_is_a_snail,axiom,
snail(a_snail),
file('theBenchmark.p',there_is_a_snail) ).
cnf(c_24,plain,
snail(a_snail),
inference(clausify,[status(thm)],[there_is_a_snail]) ).
fof(snail_is_an_animal,axiom,
! [VAR_0] :
( ~ snail(VAR_0)
| animal(VAR_0) ),
file('theBenchmark.p',snail_is_an_animal) ).
cnf(c_25,plain,
( ~ snail(A)
| animal(A) ),
inference(clausify,[status(thm)],[snail_is_an_animal]) ).
fof(snail_food_is_a_plant,axiom,
! [VAR_0] :
( ~ snail(VAR_0)
| plant(snail_food_of(VAR_0)) ),
file('theBenchmark.p',snail_food_is_a_plant) ).
cnf(c_26,plain,
( ~ snail(A)
| plant(snail_food_of(A)) ),
inference(clausify,[status(thm)],[snail_food_is_a_plant]) ).
fof(snail_eats_snail_food,axiom,
! [VAR_0] :
( ~ snail(VAR_0)
| eats(VAR_0,snail_food_of(VAR_0)) ),
file('theBenchmark.p',snail_eats_snail_food) ).
cnf(c_27,plain,
( ~ snail(A)
| eats(A,snail_food_of(A)) ),
inference(clausify,[status(thm)],[snail_eats_snail_food]) ).
cnf(c_28,plain,
( ~ snail(A)
| much_smaller(A,a_bird) ),
inference(resolve,[status(thm)],[c_15,c_11]) ).
cnf(c_29,plain,
( ~ eats(a_bird,A)
| ~ snail(A) ),
inference(resolve,[status(thm)],[c_17,c_11]) ).
fof(there_is_a_grain,axiom,
grain(a_grain),
file('theBenchmark.p',there_is_a_grain) ).
cnf(c_30,plain,
grain(a_grain),
inference(clausify,[status(thm)],[there_is_a_grain]) ).
fof(grain_is_a_plant,axiom,
! [VAR_0] :
( ~ grain(VAR_0)
| plant(VAR_0) ),
file('theBenchmark.p',grain_is_a_plant) ).
cnf(c_31,plain,
( ~ grain(A)
| plant(A) ),
inference(clausify,[status(thm)],[grain_is_a_plant]) ).
fof(prove_the_animal_exists,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ eats(VAR_1,VAR_2)
| ~ eats(VAR_0,VAR_1)
| ~ grain(VAR_2)
| ~ animal(VAR_1)
| ~ animal(VAR_0) ),
file('theBenchmark.p',prove_the_animal_exists) ).
cnf(c_32,plain,
( ~ eats(B,C)
| ~ eats(A,B)
| ~ grain(C)
| ~ animal(B)
| ~ animal(A) ),
inference(clausify,[status(thm)],[prove_the_animal_exists]) ).
cnf(c_33,plain,
( ~ eats(a_wolf,A)
| ~ grain(A) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
fof(eating_habits,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ eats(VAR_2,VAR_3)
| ~ much_smaller(VAR_2,VAR_0)
| ~ plant(VAR_3)
| ~ animal(VAR_2)
| ~ plant(VAR_1)
| ~ animal(VAR_0)
| eats(VAR_0,VAR_2)
| eats(VAR_0,VAR_1) ),
file('theBenchmark.p',eating_habits) ).
cnf(c_34,plain,
( ~ eats(C,D)
| ~ much_smaller(C,A)
| ~ plant(D)
| ~ animal(C)
| ~ plant(B)
| ~ animal(A)
| eats(A,C)
| eats(A,B) ),
inference(clausify,[status(thm)],[eating_habits]) ).
cnf(c_35,plain,
much_smaller(a_fox,a_wolf),
inference(resolve,[status(thm)],[c_6,c_8]) ).
cnf(c_37,plain,
much_smaller(a_bird,a_fox),
inference(resolve,[status(thm)],[c_11,c_13]) ).
cnf(c_38,plain,
much_smaller(a_snail,a_bird),
inference(resolve,[status(thm)],[c_28,c_24]) ).
cnf(c_39,plain,
( ~ eats(a_snail,B)
| ~ plant(B)
| ~ animal(a_snail)
| ~ plant(A)
| ~ animal(a_bird)
| eats(a_bird,a_snail)
| eats(a_bird,A) ),
inference(resolve,[status(thm)],[c_38,c_34]) ).
cnf(c_40,plain,
( ~ eats(a_bird,B)
| ~ plant(B)
| ~ animal(a_bird)
| ~ plant(A)
| ~ animal(a_fox)
| eats(a_fox,a_bird)
| eats(a_fox,A) ),
inference(resolve,[status(thm)],[c_37,c_34]) ).
cnf(c_42,plain,
( ~ eats(a_fox,B)
| ~ plant(B)
| ~ animal(a_fox)
| ~ plant(A)
| ~ animal(a_wolf)
| eats(a_wolf,a_fox)
| eats(a_wolf,A) ),
inference(resolve,[status(thm)],[c_34,c_35]) ).
cnf(c_43,plain,
~ eats(a_bird,a_snail),
inference(resolve,[status(thm)],[c_29,c_24]) ).
cnf(c_44,plain,
eats(a_snail,snail_food_of(a_snail)),
inference(resolve,[status(thm)],[c_27,c_24]) ).
cnf(c_45,plain,
plant(snail_food_of(a_snail)),
inference(resolve,[status(thm)],[c_26,c_24]) ).
cnf(c_46,plain,
animal(a_snail),
inference(resolve,[status(thm)],[c_24,c_25]) ).
cnf(c_47,plain,
animal(a_bird),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_48,plain,
animal(a_wolf),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_49,plain,
~ eats(a_wolf,a_fox),
inference(resolve,[status(thm)],[c_6,c_9]) ).
cnf(c_50,plain,
animal(a_fox),
inference(resolve,[status(thm)],[c_10,c_6]) ).
cnf(c_55,plain,
plant(a_grain),
inference(resolve,[status(thm)],[c_30,c_31]) ).
cnf(c_56,plain,
( ~ eats(B,a_grain)
| ~ eats(A,B)
| ~ animal(B)
| ~ animal(A) ),
inference(resolve,[status(thm)],[c_30,c_32]) ).
cnf(c_57,plain,
~ eats(a_wolf,a_grain),
inference(resolve,[status(thm)],[c_30,c_33]) ).
cnf(c_92,plain,
( ~ eats(a_snail,A)
| ~ animal(a_snail)
| ~ plant(A)
| ~ animal(a_bird)
| eats(a_bird,a_snail)
| eats(a_bird,A) ),
inference(factor,[status(thm)],[c_39]) ).
cnf(c_93,plain,
( ~ eats(a_snail,A)
| ~ animal(a_snail)
| ~ plant(A)
| ~ animal(a_bird)
| eats(a_bird,A) ),
inference(resolve,[status(thm)],[c_43,c_92]) ).
cnf(c_94,plain,
( ~ eats(a_snail,A)
| ~ animal(a_snail)
| ~ plant(A)
| eats(a_bird,A) ),
inference(resolve,[status(thm)],[c_47,c_93]) ).
cnf(c_59,plain,
( ~ eats(a_snail,A)
| ~ plant(A)
| eats(a_bird,A) ),
inference(resolve,[status(thm)],[c_46,c_94]) ).
cnf(c_95,plain,
( ~ eats(a_bird,A)
| ~ animal(a_bird)
| ~ plant(A)
| ~ animal(a_fox)
| eats(a_fox,a_bird)
| eats(a_fox,A) ),
inference(factor,[status(thm)],[c_40]) ).
cnf(c_96,plain,
( ~ eats(a_bird,A)
| ~ animal(a_bird)
| ~ plant(A)
| eats(a_fox,a_bird)
| eats(a_fox,A) ),
inference(resolve,[status(thm)],[c_50,c_95]) ).
cnf(c_61,plain,
( ~ eats(a_bird,A)
| ~ plant(A)
| eats(a_fox,a_bird)
| eats(a_fox,A) ),
inference(resolve,[status(thm)],[c_47,c_96]) ).
cnf(c_97,plain,
( ~ eats(a_snail,B)
| ~ plant(B)
| ~ animal(a_snail)
| ~ plant(A)
| ~ animal(a_bird)
| eats(a_bird,A) ),
inference(resolve,[status(thm)],[c_43,c_39]) ).
cnf(c_98,plain,
( ~ eats(a_snail,B)
| ~ plant(B)
| ~ animal(a_snail)
| ~ plant(A)
| eats(a_bird,A) ),
inference(resolve,[status(thm)],[c_47,c_97]) ).
cnf(c_64,plain,
( ~ eats(a_snail,B)
| ~ plant(B)
| ~ plant(A)
| eats(a_bird,A) ),
inference(resolve,[status(thm)],[c_46,c_98]) ).
cnf(c_99,plain,
( ~ eats(a_fox,B)
| ~ plant(B)
| ~ animal(a_fox)
| ~ plant(A)
| ~ animal(a_wolf)
| eats(a_wolf,A) ),
inference(resolve,[status(thm)],[c_49,c_42]) ).
cnf(c_100,plain,
( ~ eats(a_fox,B)
| ~ plant(B)
| ~ animal(a_fox)
| ~ plant(A)
| eats(a_wolf,A) ),
inference(resolve,[status(thm)],[c_48,c_99]) ).
cnf(c_66,plain,
( ~ eats(a_fox,B)
| ~ plant(B)
| ~ plant(A)
| eats(a_wolf,A) ),
inference(resolve,[status(thm)],[c_50,c_100]) ).
cnf(c_101,plain,
( ~ plant(snail_food_of(a_snail))
| eats(a_bird,snail_food_of(a_snail)) ),
inference(resolve,[status(thm)],[c_59,c_44]) ).
cnf(c_76,plain,
eats(a_bird,snail_food_of(a_snail)),
inference(resolve,[status(thm)],[c_45,c_101]) ).
cnf(c_102,plain,
( ~ plant(snail_food_of(a_snail))
| ~ plant(A)
| eats(a_bird,A) ),
inference(resolve,[status(thm)],[c_64,c_44]) ).
cnf(c_80,plain,
( ~ plant(A)
| eats(a_bird,A) ),
inference(resolve,[status(thm)],[c_45,c_102]) ).
cnf(c_103,plain,
( ~ eats(a_fox,A)
| ~ plant(A)
| ~ plant(a_grain) ),
inference(resolve,[status(thm)],[c_66,c_57]) ).
cnf(c_104,plain,
( ~ eats(a_fox,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_103,c_55]) ).
cnf(c_83,plain,
~ eats(a_fox,snail_food_of(a_snail)),
inference(resolve,[status(thm)],[c_104,c_45]) ).
cnf(c_105,plain,
( ~ plant(snail_food_of(a_snail))
| eats(a_fox,a_bird)
| eats(a_fox,snail_food_of(a_snail)) ),
inference(resolve,[status(thm)],[c_76,c_61]) ).
cnf(c_106,plain,
( ~ plant(snail_food_of(a_snail))
| eats(a_fox,a_bird) ),
inference(resolve,[status(thm)],[c_83,c_105]) ).
cnf(c_85,plain,
eats(a_fox,a_bird),
inference(resolve,[status(thm)],[c_45,c_106]) ).
cnf(c_107,plain,
( ~ eats(a_bird,a_grain)
| ~ animal(a_bird)
| ~ animal(a_fox) ),
inference(resolve,[status(thm)],[c_85,c_56]) ).
cnf(c_108,plain,
( ~ eats(a_bird,a_grain)
| ~ animal(a_bird) ),
inference(resolve,[status(thm)],[c_50,c_107]) ).
cnf(c_89,plain,
~ eats(a_bird,a_grain),
inference(resolve,[status(thm)],[c_47,c_108]) ).
cnf(c_109,plain,
eats(a_bird,a_grain),
inference(resolve,[status(thm)],[c_80,c_55]) ).
cnf(c_91,plain,
$false,
inference(resolve,[status(thm)],[c_89,c_109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ031-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n001.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sat Sep 26 05:11:41 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 970159 was started by sandbox2 on n001,
% 0.12/0.36 % Sat Sep 26 05:11:41 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.12/0.38
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.38
% 0.12/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.38 % Length of proof is 53.
% 0.12/0.38 % Level of proof is 8.
% 0.12/0.38 % Maximum clause weight is 17.000.
% 0.12/0.38 % Given clauses 36.
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------