%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ032-1 : 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 : n014.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 08:23:10 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.36s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 11 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 20 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(liars_lie,axiom,
! [VAR_0,VAR_1] :
( ~ a_truth(VAR_1)
| ~ a_truth(says(VAR_0,VAR_1))
| ~ a_truth(liar(VAR_0)) ),
file('theBenchmark.p',liars_lie) ).
cnf(c_4,plain,
( ~ a_truth(B)
| ~ a_truth(says(A,B))
| ~ a_truth(liar(A)) ),
inference(clausify,[status(thm)],[liars_lie]) ).
fof(truths_are_told_by_truthtellers,axiom,
! [VAR_0,VAR_1] :
( a_truth(truthteller(VAR_1))
| ~ a_truth(says(VAR_1,VAR_0))
| ~ a_truth(VAR_0) ),
file('theBenchmark.p',truths_are_told_by_truthtellers) ).
cnf(c_5,plain,
( a_truth(truthteller(B))
| ~ a_truth(says(B,A))
| ~ a_truth(A) ),
inference(clausify,[status(thm)],[truths_are_told_by_truthtellers]) ).
fof(liars_are_told_by_liars,axiom,
! [VAR_0,VAR_1] :
( a_truth(liar(VAR_1))
| ~ a_truth(says(VAR_1,VAR_0))
| a_truth(VAR_0) ),
file('theBenchmark.p',liars_are_told_by_liars) ).
cnf(c_6,plain,
( a_truth(liar(B))
| ~ a_truth(says(B,A))
| a_truth(A) ),
inference(clausify,[status(thm)],[liars_are_told_by_liars]) ).
fof(b_says_a_says_hes_a_liar,axiom,
a_truth(says(b,says(a,liar(a)))),
file('theBenchmark.p',b_says_a_says_hes_a_liar) ).
cnf(c_8,plain,
a_truth(says(b,says(a,liar(a)))),
inference(clausify,[status(thm)],[b_says_a_says_hes_a_liar]) ).
fof(c_says_b_is_a_liar,axiom,
a_truth(says(c,liar(b))),
file('theBenchmark.p',c_says_b_is_a_liar) ).
cnf(c_9,plain,
a_truth(says(c,liar(b))),
inference(clausify,[status(thm)],[c_says_b_is_a_liar]) ).
fof(prove_c_is_a_truthteller,axiom,
~ a_truth(truthteller(c)),
file('theBenchmark.p',prove_c_is_a_truthteller) ).
cnf(c_10,plain,
~ a_truth(truthteller(c)),
inference(clausify,[status(thm)],[prove_c_is_a_truthteller]) ).
cnf(c_11,plain,
( ~ a_truth(says(A,liar(A)))
| ~ a_truth(liar(A)) ),
inference(factor,[status(thm)],[c_4]) ).
cnf(c_12,plain,
( ~ a_truth(says(A,liar(A)))
| a_truth(liar(A)) ),
inference(factor,[status(thm)],[c_6]) ).
cnf(c_17,plain,
( a_truth(liar(b))
| a_truth(says(a,liar(a))) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
cnf(c_40,plain,
( a_truth(truthteller(c))
| ~ a_truth(liar(b)) ),
inference(resolve,[status(thm)],[c_9,c_5]) ).
cnf(c_22,plain,
~ a_truth(liar(b)),
inference(resolve,[status(thm)],[c_10,c_40]) ).
cnf(c_24,plain,
a_truth(says(a,liar(a))),
inference(resolve,[status(thm)],[c_22,c_17]) ).
cnf(c_38,plain,
a_truth(liar(a)),
inference(resolve,[status(thm)],[c_24,c_12]) ).
cnf(c_41,plain,
~ a_truth(liar(a)),
inference(resolve,[status(thm)],[c_24,c_11]) ).
cnf(c_39,plain,
$false,
inference(resolve,[status(thm)],[c_38,c_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ032-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n014.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sat Sep 26 05:06:17 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.35 % Process 2200066 was started by sandbox on n014,
% 0.10/0.35 % Sat Sep 26 05:06:17 2026
% 0.10/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.35
% 0.10/0.35 % From the command line: assign(max_seconds, 300).
% 0.10/0.36
% 0.10/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.36
% 0.10/0.36 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.36 % Length of proof is 13.
% 0.10/0.36 % Level of proof is 4.
% 0.10/0.36 % Maximum clause weight is 9.000.
% 0.10/0.36 % Given clauses 22.
% 0.10/0.36
% 0.10/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------