%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ031+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 103 ( 39 unt; 0 def)
% Number of atoms : 271 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 299 ( 131 ~; 130 |; 24 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 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(pel47_1_1,axiom,
! [X] :
( wolf(X)
=> animal(X) ),
file('theBenchmark.p',pel47_1_1) ).
fof(pel47_1_2,axiom,
? [X1] : wolf(X1),
file('theBenchmark.p',pel47_1_2) ).
fof(pel47_2_1,axiom,
! [X] :
( fox(X)
=> animal(X) ),
file('theBenchmark.p',pel47_2_1) ).
fof(pel47_2_2,axiom,
? [X1] : fox(X1),
file('theBenchmark.p',pel47_2_2) ).
fof(pel47_3_1,axiom,
! [X] :
( bird(X)
=> animal(X) ),
file('theBenchmark.p',pel47_3_1) ).
fof(pel47_3_2,axiom,
? [X1] : bird(X1),
file('theBenchmark.p',pel47_3_2) ).
fof(pel47_5_1,axiom,
! [X] :
( snail(X)
=> animal(X) ),
file('theBenchmark.p',pel47_5_1) ).
fof(pel47_5_2,axiom,
? [X1] : snail(X1),
file('theBenchmark.p',pel47_5_2) ).
fof(pel47_6_1,axiom,
? [X] : grain(X),
file('theBenchmark.p',pel47_6_1) ).
fof(pel47_6_2,axiom,
! [X1] :
( grain(X1)
=> plant(X1) ),
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,
! [X,Y] :
( ( ( caterpillar(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] :
( ( ( grain(Y)
| fox(Y) )
& wolf(X) )
=> ~ eats(X,Y) ),
file('theBenchmark.p',pel47_11) ).
fof(pel47_13,axiom,
! [X,Y] :
( ( snail(Y)
& bird(X) )
=> ~ eats(X,Y) ),
file('theBenchmark.p',pel47_13) ).
fof(pel47_14,axiom,
! [X] :
( ( snail(X)
| caterpillar(X) )
=> ? [Y] :
( eats(X,Y)
& plant(Y) ) ),
file('theBenchmark.p',pel47_14) ).
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_2,plain,
? [X1] : wolf(X1),
inference(fof_nnf,[status(thm)],[pel47_1_2]) ).
fof(sk_pel47_1_2,plain,
wolf(sK0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0)],[nnf_2]) ).
cnf(c_22,plain,
wolf(sK0),
inference(split_conjunct,[status(thm)],[sk_pel47_1_2]) ).
cnf(c_23,plain,
( animal(A)
| ~ wolf(A) ),
inference(clausify,[status(thm)],[pel47_1_1]) ).
cnf(c_24,plain,
( much_smaller(A,B)
| ~ wolf(B)
| ~ fox(A) ),
inference(clausify,[status(thm)],[pel47_10]) ).
cnf(c_25,plain,
( ~ eats(A,B)
| ~ fox(B)
| ~ wolf(A) ),
inference(clausify,[status(thm)],[pel47_11]) ).
cnf(c_26,plain,
( ~ eats(A,B)
| ~ grain(B)
| ~ wolf(A) ),
inference(clausify,[status(thm)],[pel47_11]) ).
fof(nnf_4,plain,
? [X1] : fox(X1),
inference(fof_nnf,[status(thm)],[pel47_2_2]) ).
fof(sk_pel47_2_2,plain,
fox(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1)],[nnf_4]) ).
cnf(c_27,plain,
fox(sK1),
inference(split_conjunct,[status(thm)],[sk_pel47_2_2]) ).
cnf(c_28,plain,
( much_smaller(A,B)
| ~ fox(B)
| ~ bird(A) ),
inference(clausify,[status(thm)],[pel47_9]) ).
cnf(c_29,plain,
( much_smaller(A,sK0)
| ~ fox(A) ),
inference(resolve,[status(thm)],[c_24,c_22]) ).
cnf(c_30,plain,
( ~ eats(sK0,A)
| ~ fox(A) ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_31,plain,
( animal(A)
| ~ fox(A) ),
inference(clausify,[status(thm)],[pel47_2_1]) ).
fof(nnf_6,plain,
? [X1] : bird(X1),
inference(fof_nnf,[status(thm)],[pel47_3_2]) ).
fof(sk_pel47_3_2,plain,
bird(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2)],[nnf_6]) ).
cnf(c_32,plain,
bird(sK2),
inference(split_conjunct,[status(thm)],[sk_pel47_3_2]) ).
cnf(c_33,plain,
( animal(A)
| ~ bird(A) ),
inference(clausify,[status(thm)],[pel47_3_1]) ).
cnf(c_34,plain,
( much_smaller(A,sK1)
| ~ bird(A) ),
inference(resolve,[status(thm)],[c_27,c_28]) ).
cnf(c_35,plain,
( much_smaller(B,A)
| ~ snail(B)
| ~ bird(A) ),
inference(clausify,[status(thm)],[pel47_8]) ).
cnf(c_38,plain,
( ~ eats(A,B)
| ~ snail(B)
| ~ bird(A) ),
inference(clausify,[status(thm)],[pel47_13]) ).
fof(nnf_10,plain,
? [X1] : snail(X1),
inference(fof_nnf,[status(thm)],[pel47_5_2]) ).
fof(sk_pel47_5_2,plain,
snail(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3)],[nnf_10]) ).
cnf(c_45,plain,
snail(sK3),
inference(split_conjunct,[status(thm)],[sk_pel47_5_2]) ).
cnf(c_46,plain,
( animal(A)
| ~ snail(A) ),
inference(clausify,[status(thm)],[pel47_5_1]) ).
fof(nnf_20,plain,
! [X] :
( ? [Y] :
( eats(X,Y)
& plant(Y) )
| ( ~ snail(X)
& ~ caterpillar(X) ) ),
inference(fof_nnf,[status(thm)],[pel47_14]) ).
fof(sk_pel47_14_sk,plain,
! [X] :
( ( eats(X,sK4(X))
& plant(sK4(X)) )
| ( ~ snail(X)
& ~ caterpillar(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(Y,sK4(X))],[nnf_20]) ).
fof(sk_pel47_14,plain,
( ! [VAR_0] :
( eats(VAR_0,sK4(VAR_0))
| ~ snail(VAR_0) )
& ! [VAR_0] :
( plant(sK4(VAR_0))
| ~ snail(VAR_0) )
& ! [VAR_0] :
( eats(VAR_0,sK4(VAR_0))
| ~ caterpillar(VAR_0) )
& ! [VAR_0] :
( plant(sK4(VAR_0))
| ~ caterpillar(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel47_14_sk]) ).
cnf(c_47,plain,
( plant(sK4(A))
| ~ snail(A) ),
inference(split_conjunct,[status(thm)],[sk_pel47_14]) ).
cnf(c_48,plain,
( eats(A,sK4(A))
| ~ snail(A) ),
inference(split_conjunct,[status(thm)],[sk_pel47_14]) ).
cnf(c_49,plain,
( much_smaller(A,sK2)
| ~ snail(A) ),
inference(resolve,[status(thm)],[c_35,c_32]) ).
cnf(c_50,plain,
( ~ eats(sK2,A)
| ~ snail(A) ),
inference(resolve,[status(thm)],[c_38,c_32]) ).
fof(nnf_11,plain,
? [X] : grain(X),
inference(fof_nnf,[status(thm)],[pel47_6_1]) ).
fof(sk_pel47_6_1,plain,
grain(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X,sK5)],[nnf_11]) ).
cnf(c_51,plain,
grain(sK5),
inference(split_conjunct,[status(thm)],[sk_pel47_6_1]) ).
cnf(c_52,plain,
( plant(A)
| ~ grain(A) ),
inference(clausify,[status(thm)],[pel47_6_2]) ).
cnf(c_53,negated_conjecture,
( ~ eats(A,B)
| ~ eats(B,C)
| ~ grain(C)
| ~ animal(B)
| ~ animal(A) ),
inference(clausify,[status(thm)],[pel47_neg]) ).
cnf(c_54,plain,
( ~ eats(sK0,A)
| ~ grain(A) ),
inference(resolve,[status(thm)],[c_26,c_22]) ).
cnf(c_55,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_56,plain,
much_smaller(sK1,sK0),
inference(resolve,[status(thm)],[c_27,c_29]) ).
cnf(c_58,plain,
much_smaller(sK2,sK1),
inference(resolve,[status(thm)],[c_32,c_34]) ).
cnf(c_59,plain,
much_smaller(sK3,sK2),
inference(resolve,[status(thm)],[c_49,c_45]) ).
cnf(c_60,plain,
( eats(sK2,sK3)
| ~ eats(sK3,B)
| ~ plant(B)
| ~ animal(sK3)
| eats(sK2,A)
| ~ plant(A)
| ~ animal(sK2) ),
inference(resolve,[status(thm)],[c_59,c_55]) ).
cnf(c_61,plain,
( eats(sK1,sK2)
| ~ eats(sK2,B)
| ~ plant(B)
| ~ animal(sK2)
| eats(sK1,A)
| ~ plant(A)
| ~ animal(sK1) ),
inference(resolve,[status(thm)],[c_58,c_55]) ).
cnf(c_63,plain,
( eats(sK0,sK1)
| ~ eats(sK1,B)
| ~ plant(B)
| ~ animal(sK1)
| eats(sK0,A)
| ~ plant(A)
| ~ animal(sK0) ),
inference(resolve,[status(thm)],[c_55,c_56]) ).
cnf(c_64,plain,
~ eats(sK2,sK3),
inference(resolve,[status(thm)],[c_50,c_45]) ).
cnf(c_65,plain,
eats(sK3,sK4(sK3)),
inference(resolve,[status(thm)],[c_48,c_45]) ).
cnf(c_66,plain,
plant(sK4(sK3)),
inference(resolve,[status(thm)],[c_47,c_45]) ).
cnf(c_67,plain,
animal(sK3),
inference(resolve,[status(thm)],[c_45,c_46]) ).
cnf(c_68,plain,
animal(sK2),
inference(resolve,[status(thm)],[c_32,c_33]) ).
cnf(c_69,plain,
animal(sK0),
inference(resolve,[status(thm)],[c_22,c_23]) ).
cnf(c_70,plain,
~ eats(sK0,sK1),
inference(resolve,[status(thm)],[c_27,c_30]) ).
cnf(c_71,plain,
animal(sK1),
inference(resolve,[status(thm)],[c_31,c_27]) ).
cnf(c_76,plain,
plant(sK5),
inference(resolve,[status(thm)],[c_51,c_52]) ).
cnf(c_77,negated_conjecture,
( ~ eats(A,B)
| ~ eats(B,sK5)
| ~ animal(B)
| ~ animal(A) ),
inference(resolve,[status(thm)],[c_51,c_53]) ).
cnf(c_78,plain,
~ eats(sK0,sK5),
inference(resolve,[status(thm)],[c_51,c_54]) ).
cnf(c_114,plain,
( eats(sK2,sK3)
| ~ eats(sK3,A)
| ~ animal(sK3)
| eats(sK2,A)
| ~ plant(A)
| ~ animal(sK2) ),
inference(factor,[status(thm)],[c_60]) ).
cnf(c_115,plain,
( eats(sK2,sK3)
| ~ eats(sK3,A)
| ~ animal(sK3)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_68,c_114]) ).
cnf(c_116,plain,
( eats(sK2,sK3)
| ~ eats(sK3,A)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_67,c_115]) ).
cnf(c_79,plain,
( ~ eats(sK3,A)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_64,c_116]) ).
cnf(c_117,plain,
( eats(sK1,sK2)
| ~ eats(sK2,A)
| ~ animal(sK2)
| eats(sK1,A)
| ~ plant(A)
| ~ animal(sK1) ),
inference(factor,[status(thm)],[c_61]) ).
cnf(c_118,plain,
( eats(sK1,sK2)
| ~ eats(sK2,A)
| ~ animal(sK2)
| eats(sK1,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_71,c_117]) ).
cnf(c_81,plain,
( eats(sK1,sK2)
| ~ eats(sK2,A)
| eats(sK1,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_68,c_118]) ).
cnf(c_119,plain,
( eats(sK2,sK3)
| ~ eats(sK3,B)
| ~ plant(B)
| ~ animal(sK3)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_68,c_60]) ).
cnf(c_120,plain,
( eats(sK2,sK3)
| ~ eats(sK3,B)
| ~ plant(B)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_67,c_119]) ).
cnf(c_85,plain,
( ~ eats(sK3,B)
| ~ plant(B)
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_64,c_120]) ).
cnf(c_121,plain,
( eats(sK0,sK1)
| ~ eats(sK1,B)
| ~ plant(B)
| ~ animal(sK1)
| eats(sK0,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_69,c_63]) ).
cnf(c_122,plain,
( eats(sK0,sK1)
| ~ eats(sK1,B)
| ~ plant(B)
| eats(sK0,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_71,c_121]) ).
cnf(c_87,plain,
( ~ eats(sK1,B)
| ~ plant(B)
| eats(sK0,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_70,c_122]) ).
cnf(c_123,plain,
( eats(sK2,sK4(sK3))
| ~ plant(sK4(sK3)) ),
inference(resolve,[status(thm)],[c_79,c_65]) ).
cnf(c_96,plain,
eats(sK2,sK4(sK3)),
inference(resolve,[status(thm)],[c_66,c_123]) ).
cnf(c_124,plain,
( ~ plant(sK4(sK3))
| eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_85,c_65]) ).
cnf(c_101,plain,
( eats(sK2,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_66,c_124]) ).
cnf(c_125,plain,
( ~ eats(sK1,A)
| ~ plant(A)
| eats(sK0,sK5) ),
inference(resolve,[status(thm)],[c_87,c_76]) ).
cnf(c_126,plain,
( ~ eats(sK1,A)
| ~ plant(A) ),
inference(resolve,[status(thm)],[c_125,c_78]) ).
cnf(c_104,plain,
~ eats(sK1,sK4(sK3)),
inference(resolve,[status(thm)],[c_126,c_66]) ).
cnf(c_127,plain,
( eats(sK1,sK2)
| eats(sK1,sK4(sK3))
| ~ plant(sK4(sK3)) ),
inference(resolve,[status(thm)],[c_96,c_81]) ).
cnf(c_128,plain,
( eats(sK1,sK2)
| eats(sK1,sK4(sK3)) ),
inference(resolve,[status(thm)],[c_66,c_127]) ).
cnf(c_107,plain,
eats(sK1,sK2),
inference(resolve,[status(thm)],[c_104,c_128]) ).
cnf(c_129,negated_conjecture,
( ~ eats(sK2,sK5)
| ~ animal(sK2)
| ~ animal(sK1) ),
inference(resolve,[status(thm)],[c_107,c_77]) ).
cnf(c_130,negated_conjecture,
( ~ eats(sK2,sK5)
| ~ animal(sK2) ),
inference(resolve,[status(thm)],[c_71,c_129]) ).
cnf(c_111,negated_conjecture,
~ eats(sK2,sK5),
inference(resolve,[status(thm)],[c_68,c_130]) ).
cnf(c_131,plain,
eats(sK2,sK5),
inference(resolve,[status(thm)],[c_101,c_76]) ).
cnf(c_113,plain,
$false,
inference(resolve,[status(thm)],[c_111,c_131]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ031+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 05:08:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 131952 was started by sandbox on n026,
% 0.10/0.37 % Sat Sep 26 05:08:39 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.38
% 0.10/0.38 % SZS status Theorem for theBenchmark
% 0.10/0.38
% 0.10/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.38 % Length of proof is 71.
% 0.10/0.38 % Level of proof is 9.
% 0.10/0.38 % Maximum clause weight is 17.000.
% 0.10/0.38 % Given clauses 36.
% 0.10/0.38
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------