%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ021-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 08:23:07 AM UTC 2026
% Result : Unsatisfiable 0.02s 0.31s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 10 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 108 ( 54 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 74 ( 8 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(knights_tell_truth2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ a_truth(VAR_2,VAR_1)
| says(VAR_0,VAR_2)
| ~ a_truth(knight(VAR_0),VAR_1) ),
file('theBenchmark.p',knights_tell_truth2) ).
cnf(c_1,plain,
( ~ a_truth(C,B)
| says(A,C)
| ~ a_truth(knight(A),B) ),
inference(clausify,[status(thm)],[knights_tell_truth2]) ).
fof(knights_tell_truth1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( a_truth(VAR_2,VAR_1)
| ~ says(VAR_0,VAR_2)
| ~ a_truth(knight(VAR_0),VAR_1) ),
file('theBenchmark.p',knights_tell_truth1) ).
cnf(c_2,plain,
( a_truth(C,B)
| ~ says(A,C)
| ~ a_truth(knight(A),B) ),
inference(clausify,[status(thm)],[knights_tell_truth1]) ).
fof(knaves_lie1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ a_truth(VAR_2,VAR_1)
| ~ says(VAR_0,VAR_2)
| ~ a_truth(knave(VAR_0),VAR_1) ),
file('theBenchmark.p',knaves_lie1) ).
cnf(c_3,plain,
( ~ a_truth(C,B)
| ~ says(A,C)
| ~ a_truth(knave(A),B) ),
inference(clausify,[status(thm)],[knaves_lie1]) ).
fof(knaves_lie2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( a_truth(VAR_2,VAR_1)
| says(VAR_0,VAR_2)
| ~ a_truth(knave(VAR_0),VAR_1) ),
file('theBenchmark.p',knaves_lie2) ).
cnf(c_4,plain,
( a_truth(C,B)
| says(A,C)
| ~ a_truth(knave(A),B) ),
inference(clausify,[status(thm)],[knaves_lie2]) ).
fof(prove_statement_exists1,axiom,
! [VAR_0] :
( ~ a_truth(and(knave(me),rich(me)),VAR_0)
| ~ says(me,VAR_0) ),
file('theBenchmark.p',prove_statement_exists1) ).
cnf(c_5,plain,
( ~ a_truth(and(knave(me),rich(me)),A)
| ~ says(me,A) ),
inference(clausify,[status(thm)],[prove_statement_exists1]) ).
fof(prove_statement_exists2,axiom,
! [VAR_0] :
( a_truth(and(knave(me),rich(me)),VAR_0)
| says(me,VAR_0) ),
file('theBenchmark.p',prove_statement_exists2) ).
cnf(c_6,plain,
( a_truth(and(knave(me),rich(me)),A)
| says(me,A) ),
inference(clausify,[status(thm)],[prove_statement_exists2]) ).
cnf(c_7,plain,
( a_truth(A,B)
| ~ a_truth(knight(me),B)
| a_truth(and(knave(me),rich(me)),A) ),
inference(resolve,[status(thm)],[c_6,c_2]) ).
cnf(c_8,plain,
( ~ a_truth(A,B)
| ~ a_truth(knave(me),B)
| a_truth(and(knave(me),rich(me)),A) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_9,plain,
( ~ a_truth(A,B)
| ~ a_truth(knight(me),B)
| ~ a_truth(and(knave(me),rich(me)),A) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_10,plain,
( a_truth(A,B)
| ~ a_truth(knave(me),B)
| ~ a_truth(and(knave(me),rich(me)),A) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_11,plain,
( a_truth(C,D)
| ~ a_truth(knight(A),D)
| a_truth(C,B)
| ~ a_truth(knave(A),B) ),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_12,plain,
( ~ a_truth(C,D)
| ~ a_truth(knave(A),D)
| a_truth(C,B)
| ~ a_truth(knave(A),B) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
fof(conjunction2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( a_truth(VAR_1,VAR_2)
| ~ a_truth(and(VAR_0,VAR_1),VAR_2) ),
file('theBenchmark.p',conjunction2) ).
cnf(c_16,plain,
( a_truth(B,C)
| ~ a_truth(and(A,B),C) ),
inference(clausify,[status(thm)],[conjunction2]) ).
fof(conjunction1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( a_truth(VAR_0,VAR_2)
| ~ a_truth(and(VAR_0,VAR_1),VAR_2) ),
file('theBenchmark.p',conjunction1) ).
cnf(c_17,plain,
( a_truth(A,C)
| ~ a_truth(and(A,B),C) ),
inference(clausify,[status(thm)],[conjunction1]) ).
fof(knight_or_knave,axiom,
! [VAR_0,VAR_1] :
( a_truth(knave(VAR_0),VAR_1)
| a_truth(knight(VAR_0),VAR_1) ),
file('theBenchmark.p',knight_or_knave) ).
cnf(c_20,plain,
( a_truth(knave(A),B)
| a_truth(knight(A),B) ),
inference(clausify,[status(thm)],[knight_or_knave]) ).
cnf(c_23,plain,
( ~ a_truth(knave(me),A)
| a_truth(and(knave(me),rich(me)),knave(me)) ),
inference(factor,[status(thm)],[c_8]) ).
cnf(c_48,plain,
( a_truth(B,A)
| a_truth(and(knave(me),rich(me)),B)
| a_truth(knave(me),A) ),
inference(resolve,[status(thm)],[c_20,c_7]) ).
cnf(c_49,plain,
( a_truth(and(knave(me),rich(me)),knave(me))
| a_truth(knave(me),A) ),
inference(factor,[status(thm)],[c_48]) ).
cnf(c_180,plain,
( a_truth(and(knave(me),rich(me)),knave(me))
| a_truth(and(knave(me),rich(me)),knave(me)) ),
inference(resolve,[status(thm)],[c_49,c_23]) ).
cnf(c_79,plain,
a_truth(and(knave(me),rich(me)),knave(me)),
inference(copy,[status(thm)],[c_180]) ).
cnf(c_82,plain,
( a_truth(knave(me),knave(me))
| a_truth(knave(me),A) ),
inference(resolve,[status(thm)],[c_49,c_17]) ).
cnf(c_92,plain,
a_truth(knave(me),knave(me)),
inference(factor,[status(thm)],[c_82]) ).
cnf(c_181,plain,
( ~ a_truth(knight(me),knave(me))
| ~ a_truth(and(knave(me),rich(me)),knave(me)) ),
inference(resolve,[status(thm)],[c_92,c_9]) ).
cnf(c_107,plain,
~ a_truth(knight(me),knave(me)),
inference(resolve,[status(thm)],[c_79,c_181]) ).
cnf(c_115,plain,
~ a_truth(and(A,knight(me)),knave(me)),
inference(resolve,[status(thm)],[c_16,c_107]) ).
cnf(c_182,plain,
( a_truth(A,knave(me))
| ~ a_truth(and(knave(me),rich(me)),A) ),
inference(resolve,[status(thm)],[c_10,c_92]) ).
cnf(c_116,plain,
~ a_truth(and(knave(me),rich(me)),knight(me)),
inference(resolve,[status(thm)],[c_182,c_107]) ).
cnf(c_183,plain,
( ~ a_truth(and(knave(me),rich(me)),B)
| ~ a_truth(knave(A),B)
| ~ a_truth(knave(A),knight(me)) ),
inference(resolve,[status(thm)],[c_12,c_116]) ).
cnf(c_184,plain,
( ~ a_truth(and(knave(me),rich(me)),knave(me))
| ~ a_truth(knave(me),knight(me)) ),
inference(resolve,[status(thm)],[c_183,c_92]) ).
cnf(c_136,plain,
~ a_truth(knave(me),knight(me)),
inference(resolve,[status(thm)],[c_184,c_79]) ).
cnf(c_171,plain,
~ a_truth(and(knave(me),A),knight(me)),
inference(resolve,[status(thm)],[c_17,c_136]) ).
cnf(c_185,plain,
( a_truth(A,B)
| ~ a_truth(knight(me),B)
| a_truth(A,knave(me)) ),
inference(resolve,[status(thm)],[c_11,c_92]) ).
cnf(c_186,plain,
( a_truth(and(B,knight(me)),A)
| ~ a_truth(knight(me),A) ),
inference(resolve,[status(thm)],[c_185,c_115]) ).
cnf(c_178,plain,
~ a_truth(knight(me),knight(me)),
inference(resolve,[status(thm)],[c_186,c_171]) ).
cnf(c_187,plain,
a_truth(knave(me),knight(me)),
inference(resolve,[status(thm)],[c_178,c_20]) ).
cnf(c_179,plain,
$false,
inference(resolve,[status(thm)],[c_136,c_187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : PUZ021-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sat Sep 26 05:05:06 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.30 % Process 3960389 was started by sandbox on n012,
% 0.02/0.30 % Sat Sep 26 05:05:06 2026
% 0.02/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.02/0.30
% 0.02/0.30 % From the command line: assign(max_seconds, 300).
% 0.02/0.31
% 0.02/0.31 % SZS status Unsatisfiable for theBenchmark
% 0.02/0.31
% 0.02/0.31 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.02/0.31 % Length of proof is 28.
% 0.02/0.31 % Level of proof is 11.
% 0.02/0.31 % Maximum clause weight is 14.000.
% 0.02/0.31 % Given clauses 39.
% 0.02/0.31
% 0.02/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------