%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ024-1 : 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 : 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 08:23:07 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.65s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 9 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 30 ( 11 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(b_c_a_people,axiom,
people(b,c,a),
file('theBenchmark.p',b_c_a_people) ).
cnf(c_1,plain,
people(b,c,a),
inference(clausify,[status(thm)],[b_c_a_people]) ).
fof(all_truthtellers,axiom,
! [VAR_0,VAR_1,VAR_2] :
( a_truth(truthteller(VAR_2))
| a_truth(truthteller(VAR_1))
| a_truth(truthteller(VAR_0))
| ~ people(VAR_0,VAR_1,VAR_2)
| a_truth(all_are_liars) ),
file('theBenchmark.p',all_truthtellers) ).
cnf(c_2,plain,
( a_truth(truthteller(C))
| a_truth(truthteller(B))
| a_truth(truthteller(A))
| ~ people(A,B,C)
| a_truth(all_are_liars) ),
inference(clausify,[status(thm)],[all_truthtellers]) ).
cnf(c_15,plain,
( a_truth(truthteller(a))
| a_truth(truthteller(c))
| a_truth(truthteller(b))
| a_truth(all_are_liars) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_there_is_a_truthteller,axiom,
! [VAR_0] : ~ a_truth(truthteller(VAR_0)),
file('theBenchmark.p',prove_there_is_a_truthteller) ).
cnf(c_16,plain,
~ a_truth(truthteller(A)),
inference(clausify,[status(thm)],[prove_there_is_a_truthteller]) ).
fof(a_says_all_are_liars,axiom,
a_truth(says(a,all_are_liars)),
file('theBenchmark.p',a_says_all_are_liars) ).
cnf(c_18,plain,
a_truth(says(a,all_are_liars)),
inference(clausify,[status(thm)],[a_says_all_are_liars]) ).
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_20,plain,
( a_truth(truthteller(B))
| ~ a_truth(says(B,A))
| ~ a_truth(A) ),
inference(clausify,[status(thm)],[truths_are_told_by_truthtellers]) ).
cnf(c_21,plain,
( ~ a_truth(says(B,A))
| ~ a_truth(A) ),
inference(resolve,[status(thm)],[c_16,c_20]) ).
cnf(c_27,plain,
( a_truth(truthteller(a))
| a_truth(truthteller(c))
| a_truth(all_are_liars) ),
inference(resolve,[status(thm)],[c_16,c_15]) ).
cnf(c_28,plain,
( a_truth(truthteller(a))
| a_truth(all_are_liars) ),
inference(resolve,[status(thm)],[c_16,c_27]) ).
cnf(c_24,plain,
a_truth(all_are_liars),
inference(resolve,[status(thm)],[c_16,c_28]) ).
cnf(c_29,plain,
~ a_truth(all_are_liars),
inference(resolve,[status(thm)],[c_21,c_18]) ).
cnf(c_26,plain,
$false,
inference(resolve,[status(thm)],[c_24,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ024-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.62 % Computer : n010.cluster.edu
% 0.16/0.62 % Model : x86_64 x86_64
% 0.16/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.62 % Memory : 8046.5625MB
% 0.16/0.62 % OS : Linux 6.8.0-71-generic
% 0.16/0.62 % CPULimit : 300
% 0.16/0.62 % WCLimit : 300
% 0.16/0.62 % DateTime : Sat Sep 26 05:05:31 UTC 2026
% 0.16/0.63 % CPUTime :
% 0.16/0.63 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.63 % Process 2533748 was started by sandbox2 on n010,
% 0.16/0.63 % Sat Sep 26 05:05:31 2026
% 0.16/0.63 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.64
% 0.16/0.64 % From the command line: assign(max_seconds, 300).
% 0.16/0.65
% 0.16/0.65 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.65
% 0.16/0.65 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.65 % Length of proof is 9.
% 0.16/0.65 % Level of proof is 3.
% 0.16/0.65 % Maximum clause weight is 11.000.
% 0.16/0.65 % Given clauses 4.
% 0.16/0.65
% 0.16/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------