%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ031+2 : 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 : n004.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 0.13s 0.39s
% Output : CNFRefutation 0.13s
% 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 |; 21 &)
% ( 0 <=>; 15 =>; 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(fox_type,axiom,
? [A] : fox(A),
file('theBenchmark.p',fox_type) ).
fof(bird_type,axiom,
? [A] : bird(A),
file('theBenchmark.p',bird_type) ).
fof(snail_type,axiom,
? [A] : snail(A),
file('theBenchmark.p',snail_type) ).
fof(pel47_1_1,axiom,
! [X] :
( wolf(X)
=> animal(X) ),
file('theBenchmark.p',pel47_1_1) ).
fof(pel47_2_1,axiom,
! [X] :
( fox(X)
=> animal(X) ),
file('theBenchmark.p',pel47_2_1) ).
fof(pel47_3_1,axiom,
! [X] :
( bird(X)
=> animal(X) ),
file('theBenchmark.p',pel47_3_1) ).
fof(pel47_4_2,axiom,
! [X] :
( snail(X)
=> animal(X) ),
file('theBenchmark.p',pel47_4_2) ).
fof(grain_type,axiom,
? [A] : grain(A),
file('theBenchmark.p',grain_type) ).
fof(pel47_6_2,axiom,
! [X] :
( grain(X)
=> plant(X) ),
file('theBenchmark.p',pel47_6_2) ).
fof(pel47_7,axiom,
! [X] :
( animal(X)
=> ( ! [Y1] :
( ( ? [Z] :
( eats(Y1,Z)
& plant(Z) )
& much_smaller(Y1,X)
& animal(Y1) )
=> 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]) ).
cnf(c_25,plain,
( animal(A)
| ~ wolf(A) ),
inference(clausify,[status(thm)],[pel47_1_1]) ).
fof(nnf_1,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_1]) ).
cnf(c_26,plain,
wolf(sK0),
inference(split_conjunct,[status(thm)],[sk_wolf_type]) ).
cnf(c_27,plain,
( much_smaller(A,B)
| ~ wolf(B)
| ~ fox(A) ),
inference(clausify,[status(thm)],[pel47_10]) ).
cnf(c_28,plain,
( ~ eats(A,B)
| ~ fox(B)
| ~ wolf(A) ),
inference(clausify,[status(thm)],[pel47_11]) ).
cnf(c_29,plain,
( ~ eats(A,B)
| ~ grain(B)
| ~ wolf(A) ),
inference(clausify,[status(thm)],[pel47_11a]) ).
fof(nnf_2,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_2]) ).
cnf(c_30,plain,
fox(sK1),
inference(split_conjunct,[status(thm)],[sk_fox_type]) ).
cnf(c_31,plain,
( animal(A)
| ~ fox(A) ),
inference(clausify,[status(thm)],[pel47_2_1]) ).
cnf(c_32,plain,
( much_smaller(A,B)
| ~ fox(B)
| ~ bird(A) ),
inference(clausify,[status(thm)],[pel47_9]) ).
cnf(c_33,plain,
( much_smaller(A,sK0)
| ~ fox(A) ),
inference(resolve,[status(thm)],[c_27,c_26]) ).
cnf(c_34,plain,
( ~ eats(sK0,A)
| ~ fox(A) ),
inference(resolve,[status(thm)],[c_28,c_26]) ).
fof(nnf_3,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_3]) ).
cnf(c_35,plain,
bird(sK2),
inference(split_conjunct,[status(thm)],[sk_bird_type]) ).
cnf(c_36,plain,
( much_smaller(A,sK1)
| ~ bird(A) ),
inference(resolve,[status(thm)],[c_30,c_32]) ).
cnf(c_37,plain,
( animal(A)
| ~ bird(A) ),
inference(clausify,[status(thm)],[pel47_3_1]) ).
cnf(c_38,plain,
( much_smaller(B,A)
| ~ snail(B)
| ~ bird(A) ),
inference(clausify,[status(thm)],[pel47_8]) ).
cnf(c_41,plain,
( ~ eats(A,B)
| ~ snail(B)
| ~ bird(A) ),
inference(clausify,[status(thm)],[pel47_13]) ).
cnf(c_48,plain,
( animal(A)
| ~ snail(A) ),
inference(clausify,[status(thm)],[pel47_4_2]) ).
fof(nnf_5,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_5]) ).
cnf(c_49,plain,
snail(sK3),
inference(split_conjunct,[status(thm)],[sk_snail_type]) ).
fof(nnf_23,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_23]) ).
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_50,plain,
( plant(sK4(A))
| ~ snail(A) ),
inference(split_conjunct,[status(thm)],[sk_pel47_14a]) ).
cnf(c_51,plain,
( eats(A,sK4(A))
| ~ snail(A) ),
inference(split_conjunct,[status(thm)],[sk_pel47_14a]) ).
cnf(c_52,plain,
( much_smaller(A,sK2)
| ~ snail(A) ),
inference(resolve,[status(thm)],[c_38,c_35]) ).
cnf(c_53,plain,
( ~ eats(sK2,A)
| ~ snail(A) ),
inference(resolve,[status(thm)],[c_41,c_35]) ).
fof(nnf_11,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_11]) ).
cnf(c_54,plain,
grain(sK5),
inference(split_conjunct,[status(thm)],[sk_grain_type]) ).
cnf(c_55,plain,
( plant(A)
| ~ grain(A) ),
inference(clausify,[status(thm)],[pel47_6_2]) ).
cnf(c_56,negated_conjecture,
( ~ eats(A,B)
| ~ eats(B,C)
| ~ grain(C)
| ~ animal(B)
| ~ animal(A) ),
inference(clausify,[status(thm)],[pel47_neg]) ).
cnf(c_57,plain,
( ~ eats(sK0,A)
| ~ grain(A) ),
inference(resolve,[status(thm)],[c_29,c_26]) ).
cnf(c_58,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_59,plain,
much_smaller(sK1,sK0),
inference(resolve,[status(thm)],[c_30,c_33]) ).
cnf(c_61,plain,
much_smaller(sK2,sK1),
inference(resolve,[status(thm)],[c_35,c_36]) ).
cnf(c_62,plain,
much_smaller(sK3,sK2),
inference(resolve,[status(thm)],[c_52,c_49]) ).
cnf(c_63,plain,
( eats(sK2,sK3)
| ~ eats(sK3,B)
| ~ plant(B)
| ~ animal(sK3)
| eats(sK2,A)
| ~ plant(A)
| ~ animal(sK2) ),
inference(resolve,[status(thm)],[c_62,c_58]) ).
cnf(c_64,plain,
( eats(sK1,sK2)
| ~ eats(sK2,B)
| ~ plant(B)
| ~ animal(sK2)
| eats(sK1,A)
| ~ plant(A)
| ~ animal(sK1) ),
inference(resolve,[status(thm)],[c_61,c_58]) ).
cnf(c_66,plain,
( eats(sK0,sK1)
| ~ eats(sK1,B)
| ~ plant(B)
| ~ animal(sK1)
| eats(sK0,A)
| ~ plant(A)
| ~ animal(sK0) ),
inference(resolve,[status(thm)],[c_58,c_59]) ).
cnf(c_67,plain,
~ eats(sK2,sK3),
inference(resolve,[status(thm)],[c_53,c_49]) ).
cnf(c_68,plain,
eats(sK3,sK4(sK3)),
inference(resolve,[status(thm)],[c_51,c_49]) ).
cnf(c_69,plain,
plant(sK4(sK3)),
inference(resolve,[status(thm)],[c_50,c_49]) ).
cnf(c_70,plain,
animal(sK3),
inference(resolve,[status(thm)],[c_48,c_49]) ).
cnf(c_71,plain,
animal(sK2),
inference(resolve,[status(thm)],[c_37,c_35]) ).
cnf(c_72,plain,
animal(sK0),
inference(resolve,[status(thm)],[c_25,c_26]) ).
cnf(c_73,plain,
animal(sK1),
inference(resolve,[status(thm)],[c_30,c_31]) ).
cnf(c_74,plain,
~ eats(sK0,sK1),
inference(resolve,[status(thm)],[c_30,c_34]) ).
cnf(c_79,plain,
plant(sK5),
inference(resolve,[status(thm)],[c_54,c_55]) ).
cnf(c_80,negated_conjecture,
( ~ eats(A,B)
| ~ eats(B,sK5)
| ~ animal(B)
| ~ animal(A) ),
inference(resolve,[status(thm)],[c_54,c_56]) ).
cnf(c_81,plain,
~ eats(sK0,sK5),
inference(resolve,[status(thm)],[c_54,c_57]) ).
cnf(c_117,plain,
( eats(sK2,sK3)
| ~ eats(sK3,A)
| ~ animal(sK3)
| eats(sK2,A)
| ~ plant(A)
| ~ animal(sK2) ),
inference(factor,[status(thm)],[c_63]) ).
cnf(c_118,plain,
( eats(sK2,sK3)
| ~ eats(sK3,A)
| ~ animal(sK3)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_71,c_117]) ).
cnf(c_119,plain,
( eats(sK2,sK3)
| ~ eats(sK3,A)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_70,c_118]) ).
cnf(c_82,plain,
( ~ eats(sK3,A)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_67,c_119]) ).
cnf(c_120,plain,
( eats(sK1,sK2)
| ~ eats(sK2,A)
| ~ animal(sK2)
| eats(sK1,A)
| ~ plant(A)
| ~ animal(sK1) ),
inference(factor,[status(thm)],[c_64]) ).
cnf(c_121,plain,
( eats(sK1,sK2)
| ~ eats(sK2,A)
| ~ animal(sK2)
| eats(sK1,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_73,c_120]) ).
cnf(c_84,plain,
( eats(sK1,sK2)
| ~ eats(sK2,A)
| eats(sK1,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_71,c_121]) ).
cnf(c_122,plain,
( eats(sK2,sK3)
| ~ eats(sK3,B)
| ~ plant(B)
| ~ animal(sK3)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_71,c_63]) ).
cnf(c_123,plain,
( eats(sK2,sK3)
| ~ eats(sK3,B)
| ~ plant(B)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_70,c_122]) ).
cnf(c_88,plain,
( ~ eats(sK3,B)
| ~ plant(B)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_67,c_123]) ).
cnf(c_124,plain,
( eats(sK0,sK1)
| ~ eats(sK1,B)
| ~ plant(B)
| ~ animal(sK1)
| eats(sK0,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_72,c_66]) ).
cnf(c_125,plain,
( eats(sK0,sK1)
| ~ eats(sK1,B)
| ~ plant(B)
| eats(sK0,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_73,c_124]) ).
cnf(c_90,plain,
( ~ eats(sK1,B)
| ~ plant(B)
| eats(sK0,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_74,c_125]) ).
cnf(c_126,plain,
( eats(sK2,sK4(sK3))
| ~ plant(sK4(sK3)) ),
inference(resolve,[status(thm)],[c_82,c_68]) ).
cnf(c_99,plain,
eats(sK2,sK4(sK3)),
inference(resolve,[status(thm)],[c_69,c_126]) ).
cnf(c_127,plain,
( ~ plant(sK4(sK3))
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_88,c_68]) ).
cnf(c_104,plain,
( eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_69,c_127]) ).
cnf(c_128,plain,
( ~ eats(sK1,A)
| ~ plant(A)
| eats(sK0,sK5) ),
inference(resolve,[status(thm)],[c_90,c_79]) ).
cnf(c_129,plain,
( ~ eats(sK1,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_128,c_81]) ).
cnf(c_107,plain,
~ eats(sK1,sK4(sK3)),
inference(resolve,[status(thm)],[c_129,c_69]) ).
cnf(c_130,plain,
( eats(sK1,sK2)
| eats(sK1,sK4(sK3))
| ~ plant(sK4(sK3)) ),
inference(resolve,[status(thm)],[c_99,c_84]) ).
cnf(c_131,plain,
( eats(sK1,sK2)
| eats(sK1,sK4(sK3)) ),
inference(resolve,[status(thm)],[c_69,c_130]) ).
cnf(c_110,plain,
eats(sK1,sK2),
inference(resolve,[status(thm)],[c_107,c_131]) ).
cnf(c_132,negated_conjecture,
( ~ eats(sK2,sK5)
| ~ animal(sK2)
| ~ animal(sK1) ),
inference(resolve,[status(thm)],[c_110,c_80]) ).
cnf(c_133,negated_conjecture,
( ~ eats(sK2,sK5)
| ~ animal(sK2) ),
inference(resolve,[status(thm)],[c_73,c_132]) ).
cnf(c_114,negated_conjecture,
~ eats(sK2,sK5),
inference(resolve,[status(thm)],[c_71,c_133]) ).
cnf(c_134,plain,
eats(sK2,sK5),
inference(resolve,[status(thm)],[c_104,c_79]) ).
cnf(c_116,plain,
$false,
inference(resolve,[status(thm)],[c_114,c_134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ031+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.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 05:06:07 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 873730 was started by sandbox on n004,
% 0.13/0.36 % Sat Sep 26 05:06:07 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.39 % Length of proof is 72.
% 0.13/0.39 % Level of proof is 9.
% 0.13/0.39 % Maximum clause weight is 17.000.
% 0.13/0.39 % Given clauses 36.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------