%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ001-1 : 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 08:22:41 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 13 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 25 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(butler_hates_poor,axiom,
! [VAR_0] :
( hates(butler,VAR_0)
| richer(VAR_0,agatha)
| ~ lives(VAR_0) ),
file('theBenchmark.p',butler_hates_poor) ).
cnf(c_1,plain,
( hates(butler,A)
| richer(A,agatha)
| ~ lives(A) ),
inference(clausify,[status(thm)],[butler_hates_poor]) ).
fof(butler,axiom,
lives(butler),
file('theBenchmark.p',butler) ).
cnf(c_3,plain,
lives(butler),
inference(clausify,[status(thm)],[butler]) ).
fof(poorer_killer,axiom,
! [VAR_0,VAR_1] :
( ~ richer(VAR_0,VAR_1)
| ~ killed(VAR_0,VAR_1) ),
file('theBenchmark.p',poorer_killer) ).
cnf(c_5,plain,
( ~ richer(A,B)
| ~ killed(A,B) ),
inference(clausify,[status(thm)],[poorer_killer]) ).
cnf(c_7,plain,
( hates(butler,butler)
| richer(butler,agatha) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_10,plain,
( hates(butler,butler)
| ~ killed(butler,agatha) ),
inference(resolve,[status(thm)],[c_5,c_7]) ).
fof(different_hates,axiom,
! [VAR_0] :
( ~ hates(charles,VAR_0)
| ~ hates(agatha,VAR_0) ),
file('theBenchmark.p',different_hates) ).
cnf(c_12,plain,
( ~ hates(charles,A)
| ~ hates(agatha,A) ),
inference(clausify,[status(thm)],[different_hates]) ).
fof(no_one_hates_everyone,axiom,
! [VAR_0] :
( ~ hates(VAR_0,charles)
| ~ hates(VAR_0,butler)
| ~ hates(VAR_0,agatha) ),
file('theBenchmark.p',no_one_hates_everyone) ).
cnf(c_13,plain,
( ~ hates(A,charles)
| ~ hates(A,butler)
| ~ hates(A,agatha) ),
inference(clausify,[status(thm)],[no_one_hates_everyone]) ).
fof(agatha_hates_agatha,axiom,
hates(agatha,agatha),
file('theBenchmark.p',agatha_hates_agatha) ).
cnf(c_14,plain,
hates(agatha,agatha),
inference(clausify,[status(thm)],[agatha_hates_agatha]) ).
fof(agatha_hates_charles,axiom,
hates(agatha,charles),
file('theBenchmark.p',agatha_hates_charles) ).
cnf(c_15,plain,
hates(agatha,charles),
inference(clausify,[status(thm)],[agatha_hates_charles]) ).
fof(killer_hates_victim,axiom,
! [VAR_0,VAR_1] :
( hates(VAR_0,VAR_1)
| ~ killed(VAR_0,VAR_1) ),
file('theBenchmark.p',killer_hates_victim) ).
cnf(c_16,plain,
( hates(A,B)
| ~ killed(A,B) ),
inference(clausify,[status(thm)],[killer_hates_victim]) ).
fof(same_hates,axiom,
! [VAR_0] :
( hates(butler,VAR_0)
| ~ hates(agatha,VAR_0) ),
file('theBenchmark.p',same_hates) ).
cnf(c_17,plain,
( hates(butler,A)
| ~ hates(agatha,A) ),
inference(clausify,[status(thm)],[same_hates]) ).
fof(prove_neither_charles_nor_butler_did_it,axiom,
( killed(charles,agatha)
| killed(butler,agatha) ),
file('theBenchmark.p',prove_neither_charles_nor_butler_did_it) ).
cnf(c_18,plain,
( killed(charles,agatha)
| killed(butler,agatha) ),
inference(clausify,[status(thm)],[prove_neither_charles_nor_butler_did_it]) ).
cnf(c_19,plain,
~ hates(charles,agatha),
inference(resolve,[status(thm)],[c_12,c_14]) ).
cnf(c_22,plain,
hates(butler,charles),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_23,plain,
hates(butler,agatha),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_30,plain,
( hates(charles,agatha)
| killed(butler,agatha) ),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_24,plain,
killed(butler,agatha),
inference(resolve,[status(thm)],[c_19,c_30]) ).
cnf(c_25,plain,
hates(butler,butler),
inference(resolve,[status(thm)],[c_24,c_10]) ).
cnf(c_31,plain,
( ~ hates(butler,butler)
| ~ hates(butler,agatha) ),
inference(resolve,[status(thm)],[c_22,c_13]) ).
cnf(c_32,plain,
~ hates(butler,butler),
inference(resolve,[status(thm)],[c_23,c_31]) ).
cnf(c_29,plain,
$false,
inference(resolve,[status(thm)],[c_25,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 05:08:12 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 962437 was started by sandbox2 on n001,
% 0.09/0.37 % Sat Sep 26 05:08:12 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/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 Unsatisfiable 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 18.
% 0.09/0.39 % Level of proof is 4.
% 0.09/0.39 % Maximum clause weight is 9.000.
% 0.09/0.39 % Given clauses 16.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------