%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ031+3 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 104 ( 39 unt; 0 def)
% Number of atoms : 265 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 289 ( 128 ~; 125 |; 20 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 107 ( 0 sgn 25 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(wolf_type,axiom,
? [A] : wolf(A),
file('theBenchmark.p',wolf_type) ).
fof(wolf_is_animal,axiom,
! [A] :
( wolf(A)
=> animal(A) ),
file('theBenchmark.p',wolf_is_animal) ).
fof(fox_type,axiom,
? [A] : fox(A),
file('theBenchmark.p',fox_type) ).
fof(fox_is_animal,axiom,
! [A] :
( fox(A)
=> animal(A) ),
file('theBenchmark.p',fox_is_animal) ).
fof(bird_type,axiom,
? [A] : bird(A),
file('theBenchmark.p',bird_type) ).
fof(bird_is_animal,axiom,
! [A] :
( bird(A)
=> animal(A) ),
file('theBenchmark.p',bird_is_animal) ).
fof(snail_type,axiom,
? [A] : snail(A),
file('theBenchmark.p',snail_type) ).
fof(snail_is_animal,axiom,
! [A] :
( snail(A)
=> animal(A) ),
file('theBenchmark.p',snail_is_animal) ).
fof(grain_type,axiom,
? [A] : grain(A),
file('theBenchmark.p',grain_type) ).
fof(grain_is_plant,axiom,
! [A] :
( grain(A)
=> plant(A) ),
file('theBenchmark.p',grain_is_plant) ).
fof(pel47_7,axiom,
! [X] :
( animal(X)
=> ( ! [Y1] :
( animal(Y1)
=> ( ( ? [Z] :
( eats(Y1,Z)
& plant(Z) )
& much_smaller(Y1,X) )
=> eats(X,Y1) ) )
| ! [Y] :
( plant(Y)
=> eats(X,Y) ) ) ),
file('theBenchmark.p',pel47_7) ).
fof(pel47_8,axiom,
! [Y,X] :
( ( snail(X)
& bird(Y) )
=> much_smaller(X,Y) ),
file('theBenchmark.p',pel47_8) ).
fof(pel47_9,axiom,
! [X,Y] :
( ( fox(Y)
& bird(X) )
=> much_smaller(X,Y) ),
file('theBenchmark.p',pel47_9) ).
fof(pel47_10,axiom,
! [X,Y] :
( ( wolf(Y)
& fox(X) )
=> much_smaller(X,Y) ),
file('theBenchmark.p',pel47_10) ).
fof(pel47_11,axiom,
! [X,Y] :
( ( fox(Y)
& wolf(X) )
=> ~ eats(X,Y) ),
file('theBenchmark.p',pel47_11) ).
fof(pel47_11a,axiom,
! [X,Y] :
( ( grain(Y)
& wolf(X) )
=> ~ eats(X,Y) ),
file('theBenchmark.p',pel47_11a) ).
fof(pel47_13,axiom,
! [X,Y] :
( ( snail(Y)
& bird(X) )
=> ~ eats(X,Y) ),
file('theBenchmark.p',pel47_13) ).
fof(pel47_14a,axiom,
! [X] :
( snail(X)
=> ? [Y] :
( eats(X,Y)
& plant(Y) ) ),
file('theBenchmark.p',pel47_14a) ).
fof(pel47,conjecture,
? [X,Y,Z] :
( eats(X,Y)
& eats(Y,Z)
& grain(Z)
& animal(Y)
& animal(X) ),
file('theBenchmark.p',pel47) ).
fof(pel47_neg,negated_conjecture,
~ ? [X,Y,Z] :
( eats(X,Y)
& eats(Y,Z)
& grain(Z)
& animal(Y)
& animal(X) ),
inference(assume_negation,[status(cth)],[pel47]) ).
fof(nnf_4,plain,
? [A] : wolf(A),
inference(fof_nnf,[status(thm)],[wolf_type]) ).
fof(sk_wolf_type,plain,
wolf(sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_4]) ).
cnf(c_30,plain,
wolf(sK0),
inference(split_conjunct,[status(thm)],[sk_wolf_type]) ).
cnf(c_31,plain,
( animal(A)
| ~ wolf(A) ),
inference(clausify,[status(thm)],[wolf_is_animal]) ).
cnf(c_32,plain,
( much_smaller(A,B)
| ~ wolf(B)
| ~ fox(A) ),
inference(clausify,[status(thm)],[pel47_10]) ).
cnf(c_33,plain,
( ~ eats(A,B)
| ~ fox(B)
| ~ wolf(A) ),
inference(clausify,[status(thm)],[pel47_11]) ).
cnf(c_34,plain,
( ~ eats(A,B)
| ~ grain(B)
| ~ wolf(A) ),
inference(clausify,[status(thm)],[pel47_11a]) ).
fof(nnf_6,plain,
? [A] : fox(A),
inference(fof_nnf,[status(thm)],[fox_type]) ).
fof(sk_fox_type,plain,
fox(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(A,sK1)],[nnf_6]) ).
cnf(c_35,plain,
fox(sK1),
inference(split_conjunct,[status(thm)],[sk_fox_type]) ).
cnf(c_36,plain,
( much_smaller(A,sK0)
| ~ fox(A) ),
inference(resolve,[status(thm)],[c_30,c_32]) ).
cnf(c_37,plain,
( ~ eats(sK0,A)
| ~ fox(A) ),
inference(resolve,[status(thm)],[c_30,c_33]) ).
cnf(c_38,plain,
( animal(A)
| ~ fox(A) ),
inference(clausify,[status(thm)],[fox_is_animal]) ).
cnf(c_39,plain,
( much_smaller(A,B)
| ~ fox(B)
| ~ bird(A) ),
inference(clausify,[status(thm)],[pel47_9]) ).
fof(nnf_8,plain,
? [A] : bird(A),
inference(fof_nnf,[status(thm)],[bird_type]) ).
fof(sk_bird_type,plain,
bird(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(A,sK2)],[nnf_8]) ).
cnf(c_40,plain,
bird(sK2),
inference(split_conjunct,[status(thm)],[sk_bird_type]) ).
cnf(c_41,plain,
( animal(A)
| ~ bird(A) ),
inference(clausify,[status(thm)],[bird_is_animal]) ).
cnf(c_42,plain,
( much_smaller(B,A)
| ~ snail(B)
| ~ bird(A) ),
inference(clausify,[status(thm)],[pel47_8]) ).
cnf(c_45,plain,
( ~ eats(A,B)
| ~ snail(B)
| ~ bird(A) ),
inference(clausify,[status(thm)],[pel47_13]) ).
cnf(c_46,plain,
( much_smaller(A,sK1)
| ~ bird(A) ),
inference(resolve,[status(thm)],[c_39,c_35]) ).
fof(nnf_12,plain,
? [A] : snail(A),
inference(fof_nnf,[status(thm)],[snail_type]) ).
fof(sk_snail_type,plain,
snail(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(A,sK3)],[nnf_12]) ).
cnf(c_53,plain,
snail(sK3),
inference(split_conjunct,[status(thm)],[sk_snail_type]) ).
cnf(c_54,plain,
( animal(A)
| ~ snail(A) ),
inference(clausify,[status(thm)],[snail_is_animal]) ).
fof(nnf_28,plain,
! [X] :
( ? [Y] :
( eats(X,Y)
& plant(Y) )
| ~ snail(X) ),
inference(fof_nnf,[status(thm)],[pel47_14a]) ).
fof(sk_pel47_14a_sk,plain,
! [X] :
( ( eats(X,sK4(X))
& plant(sK4(X)) )
| ~ snail(X) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(Y,sK4(X))],[nnf_28]) ).
fof(sk_pel47_14a,plain,
( ! [VAR_0] :
( eats(VAR_0,sK4(VAR_0))
| ~ snail(VAR_0) )
& ! [VAR_0] :
( plant(sK4(VAR_0))
| ~ snail(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel47_14a_sk]) ).
cnf(c_55,plain,
( plant(sK4(A))
| ~ snail(A) ),
inference(split_conjunct,[status(thm)],[sk_pel47_14a]) ).
cnf(c_56,plain,
( eats(A,sK4(A))
| ~ snail(A) ),
inference(split_conjunct,[status(thm)],[sk_pel47_14a]) ).
cnf(c_57,plain,
( much_smaller(A,sK2)
| ~ snail(A) ),
inference(resolve,[status(thm)],[c_40,c_42]) ).
cnf(c_58,plain,
( ~ eats(sK2,A)
| ~ snail(A) ),
inference(resolve,[status(thm)],[c_40,c_45]) ).
fof(nnf_16,plain,
? [A] : grain(A),
inference(fof_nnf,[status(thm)],[grain_type]) ).
fof(sk_grain_type,plain,
grain(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(A,sK5)],[nnf_16]) ).
cnf(c_59,plain,
grain(sK5),
inference(split_conjunct,[status(thm)],[sk_grain_type]) ).
cnf(c_60,plain,
( ~ eats(sK0,A)
| ~ grain(A) ),
inference(resolve,[status(thm)],[c_30,c_34]) ).
cnf(c_61,plain,
( plant(A)
| ~ grain(A) ),
inference(clausify,[status(thm)],[grain_is_plant]) ).
cnf(c_62,negated_conjecture,
( ~ eats(A,B)
| ~ eats(B,C)
| ~ grain(C)
| ~ animal(B)
| ~ animal(A) ),
inference(clausify,[status(thm)],[pel47_neg]) ).
cnf(c_63,plain,
( eats(A,C)
| ~ eats(C,D)
| ~ plant(D)
| ~ much_smaller(C,A)
| ~ animal(C)
| eats(A,B)
| ~ plant(B)
| ~ animal(A) ),
inference(clausify,[status(thm)],[pel47_7]) ).
cnf(c_64,plain,
much_smaller(sK1,sK0),
inference(resolve,[status(thm)],[c_35,c_36]) ).
cnf(c_66,plain,
much_smaller(sK2,sK1),
inference(resolve,[status(thm)],[c_40,c_46]) ).
cnf(c_67,plain,
much_smaller(sK3,sK2),
inference(resolve,[status(thm)],[c_57,c_53]) ).
cnf(c_68,plain,
( eats(sK2,sK3)
| ~ eats(sK3,B)
| ~ plant(B)
| ~ animal(sK3)
| eats(sK2,A)
| ~ plant(A)
| ~ animal(sK2) ),
inference(resolve,[status(thm)],[c_67,c_63]) ).
cnf(c_69,plain,
( eats(sK1,sK2)
| ~ eats(sK2,B)
| ~ plant(B)
| ~ animal(sK2)
| eats(sK1,A)
| ~ plant(A)
| ~ animal(sK1) ),
inference(resolve,[status(thm)],[c_66,c_63]) ).
cnf(c_71,plain,
( eats(sK0,sK1)
| ~ eats(sK1,B)
| ~ plant(B)
| ~ animal(sK1)
| eats(sK0,A)
| ~ plant(A)
| ~ animal(sK0) ),
inference(resolve,[status(thm)],[c_63,c_64]) ).
cnf(c_72,plain,
~ eats(sK2,sK3),
inference(resolve,[status(thm)],[c_58,c_53]) ).
cnf(c_73,plain,
eats(sK3,sK4(sK3)),
inference(resolve,[status(thm)],[c_53,c_56]) ).
cnf(c_74,plain,
plant(sK4(sK3)),
inference(resolve,[status(thm)],[c_53,c_55]) ).
cnf(c_75,plain,
animal(sK3),
inference(resolve,[status(thm)],[c_53,c_54]) ).
cnf(c_76,plain,
animal(sK2),
inference(resolve,[status(thm)],[c_40,c_41]) ).
cnf(c_77,plain,
animal(sK0),
inference(resolve,[status(thm)],[c_30,c_31]) ).
cnf(c_80,plain,
~ eats(sK0,sK1),
inference(resolve,[status(thm)],[c_35,c_37]) ).
cnf(c_81,plain,
animal(sK1),
inference(resolve,[status(thm)],[c_38,c_35]) ).
cnf(c_86,plain,
~ eats(sK0,sK5),
inference(resolve,[status(thm)],[c_59,c_60]) ).
cnf(c_87,plain,
plant(sK5),
inference(resolve,[status(thm)],[c_61,c_59]) ).
cnf(c_88,negated_conjecture,
( ~ eats(A,B)
| ~ eats(B,sK5)
| ~ animal(B)
| ~ animal(A) ),
inference(resolve,[status(thm)],[c_62,c_59]) ).
cnf(c_125,plain,
( eats(sK2,sK3)
| ~ eats(sK3,A)
| ~ animal(sK3)
| eats(sK2,A)
| ~ plant(A)
| ~ animal(sK2) ),
inference(factor,[status(thm)],[c_68]) ).
cnf(c_126,plain,
( eats(sK2,sK3)
| ~ eats(sK3,A)
| ~ animal(sK3)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_76,c_125]) ).
cnf(c_127,plain,
( eats(sK2,sK3)
| ~ eats(sK3,A)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_75,c_126]) ).
cnf(c_89,plain,
( ~ eats(sK3,A)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_72,c_127]) ).
cnf(c_128,plain,
( eats(sK1,sK2)
| ~ eats(sK2,A)
| ~ animal(sK2)
| eats(sK1,A)
| ~ plant(A)
| ~ animal(sK1) ),
inference(factor,[status(thm)],[c_69]) ).
cnf(c_129,plain,
( eats(sK1,sK2)
| ~ eats(sK2,A)
| ~ animal(sK2)
| eats(sK1,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_81,c_128]) ).
cnf(c_91,plain,
( eats(sK1,sK2)
| ~ eats(sK2,A)
| eats(sK1,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_76,c_129]) ).
cnf(c_130,plain,
( eats(sK2,sK3)
| ~ eats(sK3,B)
| ~ plant(B)
| ~ animal(sK3)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_76,c_68]) ).
cnf(c_131,plain,
( eats(sK2,sK3)
| ~ eats(sK3,B)
| ~ plant(B)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_75,c_130]) ).
cnf(c_95,plain,
( ~ eats(sK3,B)
| ~ plant(B)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_72,c_131]) ).
cnf(c_132,plain,
( eats(sK0,sK1)
| ~ eats(sK1,B)
| ~ plant(B)
| ~ animal(sK1)
| eats(sK0,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_77,c_71]) ).
cnf(c_133,plain,
( eats(sK0,sK1)
| ~ eats(sK1,B)
| ~ plant(B)
| eats(sK0,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_81,c_132]) ).
cnf(c_97,plain,
( ~ eats(sK1,B)
| ~ plant(B)
| eats(sK0,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_80,c_133]) ).
cnf(c_134,plain,
( eats(sK2,sK4(sK3))
| ~ plant(sK4(sK3)) ),
inference(resolve,[status(thm)],[c_89,c_73]) ).
cnf(c_106,plain,
eats(sK2,sK4(sK3)),
inference(resolve,[status(thm)],[c_74,c_134]) ).
cnf(c_135,plain,
( ~ plant(sK4(sK3))
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_95,c_73]) ).
cnf(c_111,plain,
( eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_74,c_135]) ).
cnf(c_136,plain,
( ~ eats(sK1,A)
| ~ plant(A)
| eats(sK0,sK5) ),
inference(resolve,[status(thm)],[c_97,c_87]) ).
cnf(c_137,plain,
( ~ eats(sK1,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_136,c_86]) ).
cnf(c_115,plain,
~ eats(sK1,sK4(sK3)),
inference(resolve,[status(thm)],[c_137,c_74]) ).
cnf(c_138,plain,
( eats(sK1,sK2)
| eats(sK1,sK4(sK3))
| ~ plant(sK4(sK3)) ),
inference(resolve,[status(thm)],[c_106,c_91]) ).
cnf(c_139,plain,
( eats(sK1,sK2)
| eats(sK1,sK4(sK3)) ),
inference(resolve,[status(thm)],[c_74,c_138]) ).
cnf(c_118,plain,
eats(sK1,sK2),
inference(resolve,[status(thm)],[c_115,c_139]) ).
cnf(c_140,negated_conjecture,
( ~ eats(sK2,sK5)
| ~ animal(sK2)
| ~ animal(sK1) ),
inference(resolve,[status(thm)],[c_118,c_88]) ).
cnf(c_141,negated_conjecture,
( ~ eats(sK2,sK5)
| ~ animal(sK2) ),
inference(resolve,[status(thm)],[c_81,c_140]) ).
cnf(c_122,negated_conjecture,
~ eats(sK2,sK5),
inference(resolve,[status(thm)],[c_76,c_141]) ).
cnf(c_142,plain,
eats(sK2,sK5),
inference(resolve,[status(thm)],[c_111,c_87]) ).
cnf(c_124,plain,
$false,
inference(resolve,[status(thm)],[c_122,c_142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ031+3 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 05:06:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1258497 was started by sandbox on n005,
% 0.09/0.37 % Sat Sep 26 05:06:17 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 72.
% 0.09/0.39 % Level of proof is 9.
% 0.09/0.39 % Maximum clause weight is 17.000.
% 0.09/0.39 % Given clauses 38.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------