%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ023-1 : 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 : n008.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 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 6 unt; 0 def)
% Number of atoms : 52 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 57 ( 30 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 4 ( 1 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(b_and_c_truthtellers,axiom,
( an_answer(b_and_c_truthtellers)
| ~ a_truth(truthteller(c))
| ~ a_truth(truthteller(b)) ),
file('theBenchmark.p',b_and_c_truthtellers) ).
cnf(c_9,plain,
( an_answer(b_and_c_truthtellers)
| ~ a_truth(truthteller(c))
| ~ a_truth(truthteller(b)) ),
inference(clausify,[status(thm)],[b_and_c_truthtellers]) ).
fof(prove_there_is_an_answer,axiom,
! [VAR_0] : ~ an_answer(VAR_0),
file('theBenchmark.p',prove_there_is_an_answer) ).
cnf(c_10,plain,
~ an_answer(A),
inference(clausify,[status(thm)],[prove_there_is_an_answer]) ).
fof(b_truthteller_and_c_liar,axiom,
( an_answer(b_truthteller_and_c_liar)
| ~ a_truth(liar(c))
| ~ a_truth(truthteller(b)) ),
file('theBenchmark.p',b_truthteller_and_c_liar) ).
cnf(c_11,plain,
( an_answer(b_truthteller_and_c_liar)
| ~ a_truth(liar(c))
| ~ a_truth(truthteller(b)) ),
inference(clausify,[status(thm)],[b_truthteller_and_c_liar]) ).
fof(b_liar_and_c_truthteller,axiom,
( an_answer(b_liar_and_c_truthteller)
| ~ a_truth(truthteller(c))
| ~ a_truth(liar(b)) ),
file('theBenchmark.p',b_liar_and_c_truthteller) ).
cnf(c_12,plain,
( an_answer(b_liar_and_c_truthteller)
| ~ a_truth(truthteller(c))
| ~ a_truth(liar(b)) ),
inference(clausify,[status(thm)],[b_liar_and_c_truthteller]) ).
fof(b_and_c_liars,axiom,
( an_answer(b_and_c_liars)
| ~ a_truth(liar(c))
| ~ a_truth(liar(b)) ),
file('theBenchmark.p',b_and_c_liars) ).
cnf(c_13,plain,
( an_answer(b_and_c_liars)
| ~ a_truth(liar(c))
| ~ a_truth(liar(b)) ),
inference(clausify,[status(thm)],[b_and_c_liars]) ).
cnf(c_14,plain,
( ~ a_truth(liar(c))
| ~ a_truth(liar(b)) ),
inference(resolve,[status(thm)],[c_13,c_10]) ).
cnf(c_15,plain,
( ~ a_truth(truthteller(c))
| ~ a_truth(liar(b)) ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_16,plain,
( ~ a_truth(liar(c))
| ~ a_truth(truthteller(b)) ),
inference(resolve,[status(thm)],[c_11,c_10]) ).
cnf(c_17,plain,
( ~ a_truth(truthteller(c))
| ~ a_truth(truthteller(b)) ),
inference(resolve,[status(thm)],[c_9,c_10]) ).
fof(truthteller_or_liar,axiom,
! [VAR_0] :
( a_truth(liar(VAR_0))
| a_truth(truthteller(VAR_0)) ),
file('theBenchmark.p',truthteller_or_liar) ).
cnf(c_18,plain,
( a_truth(liar(A))
| a_truth(truthteller(A)) ),
inference(clausify,[status(thm)],[truthteller_or_liar]) ).
cnf(c_35,plain,
( ~ a_truth(truthteller(b))
| a_truth(truthteller(c)) ),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_36,plain,
( ~ a_truth(truthteller(c))
| a_truth(truthteller(b)) ),
inference(resolve,[status(thm)],[c_18,c_15]) ).
cnf(c_37,plain,
( ~ a_truth(liar(b))
| a_truth(truthteller(c)) ),
inference(resolve,[status(thm)],[c_18,c_14]) ).
cnf(c_49,plain,
( a_truth(truthteller(b))
| a_truth(truthteller(c)) ),
inference(resolve,[status(thm)],[c_37,c_18]) ).
cnf(c_58,plain,
( a_truth(truthteller(b))
| a_truth(truthteller(b)) ),
inference(resolve,[status(thm)],[c_49,c_36]) ).
cnf(c_52,plain,
a_truth(truthteller(b)),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_55,plain,
a_truth(truthteller(c)),
inference(resolve,[status(thm)],[c_52,c_35]) ).
cnf(c_59,plain,
~ a_truth(truthteller(c)),
inference(resolve,[status(thm)],[c_52,c_17]) ).
cnf(c_57,plain,
$false,
inference(resolve,[status(thm)],[c_55,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ023-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.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 05:05:54 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 2825708 was started by sandbox on n008,
% 0.13/0.36 % Sat Sep 26 05:05:54 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 17.
% 0.13/0.38 % Level of proof is 6.
% 0.13/0.38 % Maximum clause weight is 6.000.
% 0.13/0.38 % Given clauses 30.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------