%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ001+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 : n010.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 : Theorem 0.14s 5.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 48 ( 21 unt; 0 def)
% Number of atoms : 86 ( 36 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 25 ~; 28 |; 3 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 27 ( 0 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel55_1,axiom,
? [X] :
( killed(X,agatha)
& lives(X) ),
file('theBenchmark.p',pel55_1) ).
fof(pel55_3,axiom,
! [X] :
( lives(X)
=> ( X = charles
| X = butler
| X = agatha ) ),
file('theBenchmark.p',pel55_3) ).
fof(pel55_4,axiom,
! [X,Y] :
( killed(X,Y)
=> hates(X,Y) ),
file('theBenchmark.p',pel55_4) ).
fof(pel55_5,axiom,
! [X,Y] :
( killed(X,Y)
=> ~ richer(X,Y) ),
file('theBenchmark.p',pel55_5) ).
fof(pel55_6,axiom,
! [X] :
( hates(agatha,X)
=> ~ hates(charles,X) ),
file('theBenchmark.p',pel55_6) ).
fof(pel55_7,axiom,
! [X] :
( X != butler
=> hates(agatha,X) ),
file('theBenchmark.p',pel55_7) ).
fof(pel55_8,axiom,
! [X] :
( ~ richer(X,agatha)
=> hates(butler,X) ),
file('theBenchmark.p',pel55_8) ).
fof(pel55_9,axiom,
! [X] :
( hates(agatha,X)
=> hates(butler,X) ),
file('theBenchmark.p',pel55_9) ).
fof(pel55_10,axiom,
! [X] :
? [Y] : ~ hates(X,Y),
file('theBenchmark.p',pel55_10) ).
fof(pel55,conjecture,
killed(agatha,agatha),
file('theBenchmark.p',pel55) ).
fof(pel55_neg,negated_conjecture,
~ killed(agatha,agatha),
inference(assume_negation,[status(cth)],[pel55]) ).
cnf(c_11,plain,
( charles = A
| butler = A
| agatha = A
| ~ lives(A) ),
inference(clausify,[status(thm)],[pel55_3]) ).
fof(nnf_1,plain,
? [X] :
( killed(X,agatha)
& lives(X) ),
inference(fof_nnf,[status(thm)],[pel55_1]) ).
fof(sk_pel55_1,plain,
( killed(sK0,agatha)
& lives(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_1]) ).
cnf(c_15,plain,
lives(sK0),
inference(split_conjunct,[status(thm)],[sk_pel55_1]) ).
cnf(c_16,plain,
( ~ richer(A,B)
| ~ killed(A,B) ),
inference(clausify,[status(thm)],[pel55_5]) ).
cnf(c_17,plain,
( hates(butler,A)
| richer(A,agatha) ),
inference(clausify,[status(thm)],[pel55_8]) ).
cnf(c_18,plain,
( hates(butler,A)
| ~ killed(A,agatha) ),
inference(resolve,[status(thm)],[c_16,c_17]) ).
cnf(c_19,plain,
killed(sK0,agatha),
inference(split_conjunct,[status(thm)],[sk_pel55_1]) ).
cnf(c_20,plain,
( hates(A,B)
| ~ killed(A,B) ),
inference(clausify,[status(thm)],[pel55_4]) ).
cnf(c_21,plain,
( ~ hates(charles,A)
| ~ hates(agatha,A) ),
inference(clausify,[status(thm)],[pel55_6]) ).
cnf(c_22,plain,
( hates(agatha,A)
| butler = A ),
inference(clausify,[status(thm)],[pel55_7]) ).
cnf(c_23,plain,
( hates(butler,A)
| ~ hates(agatha,A) ),
inference(clausify,[status(thm)],[pel55_9]) ).
fof(nnf_9,plain,
! [X] :
? [Y] : ~ hates(X,Y),
inference(fof_nnf,[status(thm)],[pel55_10]) ).
fof(sk_pel55_10,plain,
! [X] : ~ hates(X,sK1(X)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(Y,sK1(X))],[nnf_9]) ).
cnf(c_24,plain,
~ hates(A,sK1(A)),
inference(split_conjunct,[status(thm)],[sk_pel55_10]) ).
fof(pel55_11,axiom,
agatha != butler,
file('theBenchmark.p',pel55_11) ).
cnf(c_25,plain,
agatha != butler,
inference(clausify,[status(thm)],[pel55_11]) ).
cnf(c_26,plain,
butler != agatha,
inference(copy,[status(thm)],[c_25]) ).
cnf(c_27,negated_conjecture,
~ killed(agatha,agatha),
inference(clausify,[status(thm)],[pel55_neg]) ).
cnf(c_30,plain,
( charles = sK0
| butler = sK0
| agatha = sK0 ),
inference(resolve,[status(thm)],[c_11,c_15]) ).
cnf(c_54,plain,
( charles = sK0
| butler = sK0
| sK0 = agatha ),
inference(copy,[status(thm)],[c_30]) ).
cnf(c_55,plain,
( charles = sK0
| sK0 = butler
| sK0 = agatha ),
inference(copy,[status(thm)],[c_54]) ).
cnf(c_31,plain,
( sK0 = charles
| sK0 = butler
| sK0 = agatha ),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_33,plain,
hates(sK0,agatha),
inference(resolve,[status(thm)],[c_20,c_19]) ).
cnf(c_36,plain,
~ hates(agatha,sK1(butler)),
inference(resolve,[status(thm)],[c_23,c_24]) ).
cnf(c_38,plain,
~ killed(sK1(butler),agatha),
inference(resolve,[status(thm)],[c_18,c_24]) ).
cnf(c_56,plain,
butler = sK1(butler),
inference(resolve,[status(thm)],[c_36,c_22]) ).
cnf(c_41,plain,
sK1(butler) = butler,
inference(copy,[status(thm)],[c_56]) ).
cnf(c_43,plain,
~ killed(butler,agatha),
inference(paramod,[status(thm)],[c_41,c_38]) ).
cnf(c_45,plain,
( hates(charles,agatha)
| sK0 = butler
| sK0 = agatha ),
inference(paramod,[status(thm)],[c_31,c_33]) ).
cnf(c_48,plain,
( ~ hates(agatha,agatha)
| sK0 = butler
| sK0 = agatha ),
inference(resolve,[status(thm)],[c_45,c_21]) ).
cnf(c_57,plain,
( butler = agatha
| sK0 = butler
| sK0 = agatha ),
inference(resolve,[status(thm)],[c_48,c_22]) ).
cnf(c_49,plain,
( sK0 = butler
| sK0 = agatha ),
inference(resolve,[status(thm)],[c_26,c_57]) ).
cnf(c_58,plain,
( killed(butler,agatha)
| sK0 = agatha ),
inference(paramod,[status(thm)],[c_49,c_19]) ).
cnf(c_50,plain,
sK0 = agatha,
inference(resolve,[status(thm)],[c_43,c_58]) ).
cnf(c_59,plain,
killed(agatha,agatha),
inference(paramod,[status(thm)],[c_50,c_19]) ).
cnf(c_53,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_27,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ001+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n010.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 05:02:50 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 2529733 was started by sandbox on n010,
% 0.11/5.39 % Sat Sep 26 05:02:50 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.14/5.40
% 0.14/5.40 % SZS status Theorem for theBenchmark
% 0.14/5.40
% 0.14/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/5.40 % Length of proof is 36.
% 0.14/5.40 % Level of proof is 8.
% 0.14/5.40 % Maximum clause weight is 9.000.
% 0.14/5.40 % Given clauses 27.
% 0.14/5.40
% 0.14/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------