%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ061+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 08:23:15 AM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 7 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 119 ( 34 ~; 26 |; 47 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 65 ( 2 sgn 50 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
! [Peanuts,John,Bill,Sue,Apples,Chicken] :
( ( ! [Y] :
( alive(Y)
=> ! [X] : not_killed_by(Y,X) )
& ! [X] :
( eats(Bill,X)
=> eats(Sue,X) )
& alive(Bill)
& eats(Bill,Peanuts)
& ! [X] :
( ? [Y] :
( not_killed_by(Y,X)
& eats(Y,X) )
=> food(X) )
& food(Chicken)
& food(Apples)
& ! [X] :
( food(X)
=> likes(John,X) )
& ! [X,Y] :
( ( eats(Y,Chicken)
& alive(Y) )
=> likes(Y,X) ) )
=> likes(John,Peanuts) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ! [Peanuts,John,Bill,Sue,Apples,Chicken] :
( ( ! [Y] :
( alive(Y)
=> ! [X] : not_killed_by(Y,X) )
& ! [X] :
( eats(Bill,X)
=> eats(Sue,X) )
& alive(Bill)
& eats(Bill,Peanuts)
& ! [X] :
( ? [Y] :
( not_killed_by(Y,X)
& eats(Y,X) )
=> food(X) )
& food(Chicken)
& food(Apples)
& ! [X] :
( food(X)
=> likes(John,X) )
& ! [X,Y] :
( ( eats(Y,Chicken)
& alive(Y) )
=> likes(Y,X) ) )
=> likes(John,Peanuts) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
? [Peanuts,John,Bill,Sue,Apples,Chicken] :
( ~ likes(John,Peanuts)
& ! [Y] :
( ! [X] : not_killed_by(Y,X)
| ~ alive(Y) )
& ! [X5] :
( eats(Sue,X5)
| ~ eats(Bill,X5) )
& alive(Bill)
& eats(Bill,Peanuts)
& ! [X3] :
( food(X3)
| ! [X4] :
( ~ not_killed_by(X4,X3)
| ~ eats(X4,X3) ) )
& food(Chicken)
& food(Apples)
& ! [X2] :
( likes(John,X2)
| ~ food(X2) )
& ! [X0,X1] :
( likes(X1,X0)
| ~ eats(X1,Chicken)
| ~ alive(X1) ) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg_sk,plain,
( ~ likes(sK1,sK2)
& ! [Y] :
( ! [X] : not_killed_by(Y,X)
| ~ alive(Y) )
& ! [X5] :
( eats(sK5,X5)
| ~ eats(sK0,X5) )
& alive(sK0)
& eats(sK0,sK2)
& ! [X3] :
( food(X3)
| ! [X4] :
( ~ not_killed_by(X4,X3)
| ~ eats(X4,X3) ) )
& food(sK3)
& food(sK4)
& ! [X2] :
( likes(sK1,X2)
| ~ food(X2) )
& ! [X0,X1] :
( likes(X1,X0)
| ~ eats(X1,sK3)
| ~ alive(X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK1,sK4,sK0,sK2,sK5]),skolemize(Peanuts,sK2),skolemize(John,sK1),skolemize(Bill,sK0),skolemize(Sue,sK5),skolemize(Apples,sK4),skolemize(Chicken,sK3)],[nnf_1]) ).
fof(sk_prove_this_neg,plain,
( ~ likes(sK1,sK2)
& ! [VAR_0,VAR_1] :
( not_killed_by(VAR_0,VAR_1)
| ~ alive(VAR_0) )
& ! [VAR_0] :
( eats(sK5,VAR_0)
| ~ eats(sK0,VAR_0) )
& alive(sK0)
& eats(sK0,sK2)
& ! [VAR_0,VAR_1] :
( food(VAR_1)
| ~ not_killed_by(VAR_0,VAR_1)
| ~ eats(VAR_0,VAR_1) )
& food(sK3)
& food(sK4)
& ! [VAR_0] :
( likes(sK1,VAR_0)
| ~ food(VAR_0) )
& ! [VAR_0,VAR_1] :
( likes(VAR_0,VAR_1)
| ~ eats(VAR_0,sK3)
| ~ alive(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_prove_this_neg_sk]) ).
cnf(c_2,negated_conjecture,
alive(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,negated_conjecture,
( not_killed_by(A,B)
| ~ alive(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_5,negated_conjecture,
~ likes(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_7,negated_conjecture,
( likes(sK1,A)
| ~ food(A) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_9,negated_conjecture,
~ food(sK2),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_11,negated_conjecture,
( food(B)
| ~ not_killed_by(A,B)
| ~ eats(A,B) ),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_12,negated_conjecture,
not_killed_by(sK0,A),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_13,negated_conjecture,
( ~ not_killed_by(A,sK2)
| ~ eats(A,sK2) ),
inference(resolve,[status(thm)],[c_11,c_9]) ).
cnf(c_14,negated_conjecture,
~ eats(sK0,sK2),
inference(resolve,[status(thm)],[c_12,c_13]) ).
cnf(c_15,negated_conjecture,
eats(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_16,plain,
$false,
inference(resolve,[status(thm)],[c_15,c_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ061+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.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 05:13:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 894422 was started by sandbox on n002,
% 0.09/0.36 % Sat Sep 26 05:13:35 2026
% 0.09/0.36 % 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).
% 0.14/0.38
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.38 % Length of proof is 12.
% 0.14/0.38 % Level of proof is 5.
% 0.14/0.38 % Maximum clause weight is 3.000.
% 0.14/0.38 % Given clauses 0.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------