%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ025-1 : 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 : n013.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 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 81 ( 40 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_there_is_an_answer,axiom,
! [VAR_0] : ~ answer(VAR_0),
file('theBenchmark.p',prove_there_is_an_answer) ).
cnf(c_1,plain,
~ answer(A),
inference(clausify,[status(thm)],[prove_there_is_an_answer]) ).
fof(liar_supports_lies,axiom,
! [VAR_0,VAR_1] :
( answer(yes)
| a_truth(VAR_1)
| ~ a_truth(liar(VAR_0))
| ~ ask_1_if_2(VAR_0,VAR_1) ),
file('theBenchmark.p',liar_supports_lies) ).
cnf(c_2,plain,
( answer(yes)
| a_truth(B)
| ~ a_truth(liar(A))
| ~ ask_1_if_2(A,B) ),
inference(clausify,[status(thm)],[liar_supports_lies]) ).
fof(liar_denies_truths,axiom,
! [VAR_0,VAR_1] :
( answer(no)
| ~ a_truth(VAR_1)
| ~ a_truth(liar(VAR_0))
| ~ ask_1_if_2(VAR_0,VAR_1) ),
file('theBenchmark.p',liar_denies_truths) ).
cnf(c_3,plain,
( answer(no)
| ~ a_truth(B)
| ~ a_truth(liar(A))
| ~ ask_1_if_2(A,B) ),
inference(clausify,[status(thm)],[liar_denies_truths]) ).
fof(truthteller_denies_lies,axiom,
! [VAR_0,VAR_1] :
( answer(no)
| a_truth(VAR_1)
| ~ a_truth(truthteller(VAR_0))
| ~ ask_1_if_2(VAR_0,VAR_1) ),
file('theBenchmark.p',truthteller_denies_lies) ).
cnf(c_4,plain,
( answer(no)
| a_truth(B)
| ~ a_truth(truthteller(A))
| ~ ask_1_if_2(A,B) ),
inference(clausify,[status(thm)],[truthteller_denies_lies]) ).
fof(truthteller_identifies_truths,axiom,
! [VAR_0,VAR_1] :
( answer(yes)
| ~ a_truth(VAR_1)
| ~ a_truth(truthteller(VAR_0))
| ~ ask_1_if_2(VAR_0,VAR_1) ),
file('theBenchmark.p',truthteller_identifies_truths) ).
cnf(c_5,plain,
( answer(yes)
| ~ a_truth(B)
| ~ a_truth(truthteller(A))
| ~ ask_1_if_2(A,B) ),
inference(clausify,[status(thm)],[truthteller_identifies_truths]) ).
cnf(c_12,plain,
( a_truth(B)
| ~ a_truth(liar(A))
| ~ ask_1_if_2(A,B) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(ask_c_if_a_and_b_equal,axiom,
ask_1_if_2(c,equal_type(a,b)),
file('theBenchmark.p',ask_c_if_a_and_b_equal) ).
cnf(c_13,plain,
ask_1_if_2(c,equal_type(a,b)),
inference(clausify,[status(thm)],[ask_c_if_a_and_b_equal]) ).
cnf(c_14,plain,
( ~ a_truth(B)
| ~ a_truth(liar(A))
| ~ ask_1_if_2(A,B) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_15,plain,
( a_truth(B)
| ~ a_truth(truthteller(A))
| ~ ask_1_if_2(A,B) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_16,plain,
( ~ a_truth(B)
| ~ a_truth(truthteller(A))
| ~ ask_1_if_2(A,B) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_17,plain,
( ~ a_truth(equal_type(a,b))
| ~ a_truth(truthteller(c)) ),
inference(resolve,[status(thm)],[c_16,c_13]) ).
cnf(c_18,plain,
( a_truth(equal_type(a,b))
| ~ a_truth(truthteller(c)) ),
inference(resolve,[status(thm)],[c_15,c_13]) ).
cnf(c_19,plain,
( ~ a_truth(equal_type(a,b))
| ~ a_truth(liar(c)) ),
inference(resolve,[status(thm)],[c_14,c_13]) ).
cnf(c_20,plain,
( a_truth(equal_type(a,b))
| ~ a_truth(liar(c)) ),
inference(resolve,[status(thm)],[c_12,c_13]) ).
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_32,plain,
( a_truth(liar(A))
| a_truth(truthteller(A)) ),
inference(clausify,[status(thm)],[truthteller_or_liar]) ).
cnf(c_49,plain,
( a_truth(equal_type(a,b))
| a_truth(truthteller(c)) ),
inference(resolve,[status(thm)],[c_32,c_20]) ).
cnf(c_50,plain,
( ~ a_truth(equal_type(a,b))
| a_truth(truthteller(c)) ),
inference(resolve,[status(thm)],[c_32,c_19]) ).
cnf(c_69,plain,
( a_truth(equal_type(a,b))
| a_truth(equal_type(a,b)) ),
inference(resolve,[status(thm)],[c_49,c_18]) ).
cnf(c_65,plain,
a_truth(equal_type(a,b)),
inference(copy,[status(thm)],[c_69]) ).
cnf(c_66,plain,
a_truth(truthteller(c)),
inference(resolve,[status(thm)],[c_65,c_50]) ).
cnf(c_70,plain,
~ a_truth(equal_type(a,b)),
inference(resolve,[status(thm)],[c_66,c_17]) ).
cnf(c_68,plain,
$false,
inference(resolve,[status(thm)],[c_65,c_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ025-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n013.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 05:04:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 1973152 was started by sandbox2 on n013,
% 0.09/0.38 % Sat Sep 26 05:04:36 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 20.
% 0.09/0.39 % Level of proof is 6.
% 0.09/0.39 % Maximum clause weight is 7.000.
% 0.09/0.39 % Given clauses 31.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------