%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : PUZ023-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 08:22:05 AM UTC 2026
% Result : Unsatisfiable 15.62s 2.73s
% Output : CNFRefutation 15.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of clauses : 24 ( 6 unt; 4 nHn; 22 RR)
% Number of literals : 50 ( 0 equ; 30 neg)
% Maximal clause size : 3 ( 2 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 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_and_c_liars,hypothesis,
( 'an$uanswer'('b$uand$uc$uliars')
| ~ 'a$utruth'(liar(c))
| ~ 'a$utruth'(liar(b)) ) ).
cnf(b_liar_and_c_truthteller,hypothesis,
( 'an$uanswer'('b$uliar$uand$uc$utruthteller')
| ~ 'a$utruth'(truthteller(c))
| ~ 'a$utruth'(liar(b)) ) ).
cnf(b_truthteller_and_c_liar,hypothesis,
( 'an$uanswer'('b$utruthteller$uand$uc$uliar')
| ~ 'a$utruth'(liar(c))
| ~ 'a$utruth'(truthteller(b)) ) ).
cnf(b_and_c_truthtellers,hypothesis,
( 'an$uanswer'('b$uand$uc$utruthtellers')
| ~ 'a$utruth'(truthteller(c))
| ~ 'a$utruth'(truthteller(b)) ) ).
cnf(prove_there_is_an_answer,negated_conjecture,
~ 'an$uanswer'(X0) ).
cnf(truthteller_or_liar,axiom,
( 'a$utruth'(liar(X0))
| 'a$utruth'(truthteller(X0)) ) ).
cnf(c11,plain,
( 'an$uanswer'('b$uand$uc$uliars')
| ~ 'a$utruth'(liar(c))
| ~ 'a$utruth'(liar(b)) ),
inference(clausification,[status(esa)],[b_and_c_liars]) ).
cnf(c12,plain,
( 'an$uanswer'('b$uliar$uand$uc$utruthteller')
| ~ 'a$utruth'(truthteller(c))
| ~ 'a$utruth'(liar(b)) ),
inference(clausification,[status(esa)],[b_liar_and_c_truthteller]) ).
cnf(c13,plain,
( 'an$uanswer'('b$utruthteller$uand$uc$uliar')
| ~ 'a$utruth'(liar(c))
| ~ 'a$utruth'(truthteller(b)) ),
inference(clausification,[status(esa)],[b_truthteller_and_c_liar]) ).
cnf(c14,plain,
( 'an$uanswer'('b$uand$uc$utruthtellers')
| ~ 'a$utruth'(truthteller(c))
| ~ 'a$utruth'(truthteller(b)) ),
inference(clausification,[status(esa)],[b_and_c_truthtellers]) ).
cnf(c15,plain,
~ 'an$uanswer'(X0),
inference(clausification,[status(esa)],[prove_there_is_an_answer]) ).
cnf(c16,plain,
( 'a$utruth'(liar(X0))
| 'a$utruth'(truthteller(X0)) ),
inference(clausification,[status(esa)],[truthteller_or_liar]) ).
cnf(d0,plain,
( ~ 'a$utruth'(liar(c))
| ~ 'a$utruth'(truthteller(b)) ),
inference(resolution,[status(thm)],[c15,c13]) ).
cnf(d1,plain,
( ~ 'a$utruth'(liar(b))
| ~ 'a$utruth'(truthteller(c)) ),
inference(resolution,[status(thm)],[c15,c12]) ).
cnf(d2,plain,
( 'a$utruth'(truthteller(b))
| ~ 'a$utruth'(truthteller(c)) ),
inference(resolution,[status(thm)],[d1,c16]) ).
cnf(d3,plain,
( ~ 'a$utruth'(liar(c))
| ~ 'a$utruth'(liar(b)) ),
inference(resolution,[status(thm)],[c15,c11]) ).
cnf(d4,plain,
( 'a$utruth'(truthteller(c))
| ~ 'a$utruth'(liar(b)) ),
inference(resolution,[status(thm)],[d3,c16]) ).
cnf(d5,plain,
( 'a$utruth'(truthteller(b))
| 'a$utruth'(truthteller(c)) ),
inference(resolution,[status(thm)],[d4,c16]) ).
cnf(d6,plain,
( 'a$utruth'(truthteller(b))
| 'a$utruth'(truthteller(b)) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
~ 'a$utruth'(liar(c)),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
'a$utruth'(truthteller(c)),
inference(resolution,[status(thm)],[d7,c16]) ).
cnf(d9,plain,
( ~ 'a$utruth'(truthteller(c))
| ~ 'a$utruth'(truthteller(b)) ),
inference(resolution,[status(thm)],[c15,c14]) ).
cnf(d10,plain,
~ 'a$utruth'(truthteller(c)),
inference(resolution,[status(thm)],[d6,d9]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ023-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n001.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 05:10:57 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.62/2.73 % SZS status Unsatisfiable for theBenchmark.p
% 15.62/2.73 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------