%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : PUZ027-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 08:22:06 AM UTC 2026
% Result : Unsatisfiable 10.70s 2.02s
% Output : CNFRefutation 10.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 46 ( 9 unt; 9 nHn; 42 RR)
% Number of literals : 99 ( 0 equ; 58 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 24 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(not_lower_or_lower,axiom,
( 'a$utruth'(lower(X0,X1))
| 'a$utruth'('not$ulower'(X0,X1)) ) ).
cnf(truthtellers_lower_than_no_one,axiom,
( ~ 'a$utruth'(truthteller(X0))
| ~ 'a$utruth'(lower(X0,X1)) ) ).
cnf(no_one_lower_than_liars,axiom,
( ~ 'a$utruth'(liar(X1))
| ~ 'a$utruth'(lower(X0,X1)) ) ).
cnf(a_says_a_lower_than_b,hypothesis,
'a$utruth'(says(a,lower(a,b))) ).
cnf(b_says_a_not_lower_than_b,hypothesis,
'a$utruth'(says(b,'not$ulower'(a,b))) ).
cnf(a_normal_b_truthteller,hypothesis,
( answer('a$unormal$ub$utruthteller')
| ~ 'a$utruth'(truthteller(b))
| ~ 'a$utruth'(normal(a)) ) ).
cnf(a_and_b_normal,hypothesis,
( answer('a$uand$ub$unormal')
| ~ 'a$utruth'(normal(b))
| ~ 'a$utruth'(normal(a)) ) ).
cnf(a_liar_b_truthteller,hypothesis,
( answer('a$uliar$ub$utruthteller')
| ~ 'a$utruth'(truthteller(b))
| ~ 'a$utruth'(liar(a)) ) ).
cnf(a_liar_b_normal,hypothesis,
( answer('a$uliar$ub$unormal')
| ~ 'a$utruth'(normal(b))
| ~ 'a$utruth'(liar(a)) ) ).
cnf(prove_there_is_an_answer,negated_conjecture,
~ answer(X0) ).
cnf(person_is_one_type,axiom,
( 'a$utruth'(normal(X0))
| 'a$utruth'(liar(X0))
| 'a$utruth'(truthteller(X0)) ) ).
cnf(truthtellers_tell_truth,axiom,
( 'a$utruth'(X1)
| ~ 'a$utruth'(says(X0,X1))
| ~ 'a$utruth'(truthteller(X0)) ) ).
cnf(liars_lie,axiom,
( ~ 'a$utruth'(X1)
| ~ 'a$utruth'(says(X0,X1))
| ~ 'a$utruth'(liar(X0)) ) ).
cnf(c2,plain,
( 'a$utruth'(lower(X0,X1))
| 'a$utruth'('not$ulower'(X0,X1)) ),
inference(clausification,[status(esa)],[not_lower_or_lower]) ).
cnf(c5,plain,
( ~ 'a$utruth'(truthteller(X0))
| ~ 'a$utruth'(lower(X0,X1)) ),
inference(clausification,[status(esa)],[truthtellers_lower_than_no_one]) ).
cnf(c8,plain,
( ~ 'a$utruth'(liar(X1))
| ~ 'a$utruth'(lower(X0,X1)) ),
inference(clausification,[status(esa)],[no_one_lower_than_liars]) ).
cnf(c12,plain,
'a$utruth'(says(a,lower(a,b))),
inference(clausification,[status(esa)],[a_says_a_lower_than_b]) ).
cnf(c13,plain,
'a$utruth'(says(b,'not$ulower'(a,b))),
inference(clausification,[status(esa)],[b_says_a_not_lower_than_b]) ).
cnf(c17,plain,
( answer('a$unormal$ub$utruthteller')
| ~ 'a$utruth'(truthteller(b))
| ~ 'a$utruth'(normal(a)) ),
inference(clausification,[status(esa)],[a_normal_b_truthteller]) ).
cnf(c18,plain,
( answer('a$uand$ub$unormal')
| ~ 'a$utruth'(normal(b))
| ~ 'a$utruth'(normal(a)) ),
inference(clausification,[status(esa)],[a_and_b_normal]) ).
cnf(c20,plain,
( answer('a$uliar$ub$utruthteller')
| ~ 'a$utruth'(truthteller(b))
| ~ 'a$utruth'(liar(a)) ),
inference(clausification,[status(esa)],[a_liar_b_truthteller]) ).
cnf(c21,plain,
( answer('a$uliar$ub$unormal')
| ~ 'a$utruth'(normal(b))
| ~ 'a$utruth'(liar(a)) ),
inference(clausification,[status(esa)],[a_liar_b_normal]) ).
cnf(c23,plain,
~ answer(X0),
inference(clausification,[status(esa)],[prove_there_is_an_answer]) ).
cnf(c24,plain,
( 'a$utruth'(normal(X0))
| 'a$utruth'(liar(X0))
| 'a$utruth'(truthteller(X0)) ),
inference(clausification,[status(esa)],[person_is_one_type]) ).
cnf(c28,plain,
( 'a$utruth'(X1)
| ~ 'a$utruth'(says(X0,X1))
| ~ 'a$utruth'(truthteller(X0)) ),
inference(clausification,[status(esa)],[truthtellers_tell_truth]) ).
cnf(c29,plain,
( ~ 'a$utruth'(X1)
| ~ 'a$utruth'(says(X0,X1))
| ~ 'a$utruth'(liar(X0)) ),
inference(clausification,[status(esa)],[liars_lie]) ).
cnf(d0,plain,
( ~ 'a$utruth'(truthteller(b))
| ~ 'a$utruth'(liar(a)) ),
inference(resolution,[status(thm)],[c23,c20]) ).
cnf(d1,plain,
( ~ 'a$utruth'(liar(a))
| 'a$utruth'(normal(b))
| 'a$utruth'(liar(b)) ),
inference(resolution,[status(thm)],[c24,d0]) ).
cnf(d2,plain,
( ~ 'a$utruth'(liar(b))
| ~ 'a$utruth'('not$ulower'(a,b)) ),
inference(resolution,[status(thm)],[c29,c13]) ).
cnf(d3,plain,
( 'a$utruth'(lower(a,b))
| ~ 'a$utruth'(liar(b)) ),
inference(resolution,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
( ~ 'a$utruth'(liar(b))
| ~ 'a$utruth'(liar(b)) ),
inference(resolution,[status(thm)],[d3,c8]) ).
cnf(d5,plain,
( 'a$utruth'(normal(b))
| ~ 'a$utruth'(liar(a)) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( ~ 'a$utruth'(truthteller(a))
| 'a$utruth'(lower(a,b)) ),
inference(resolution,[status(thm)],[c28,c12]) ).
cnf(d7,plain,
( ~ 'a$utruth'(truthteller(a))
| ~ 'a$utruth'(truthteller(a)) ),
inference(resolution,[status(thm)],[d6,c5]) ).
cnf(d8,plain,
( 'a$utruth'(normal(a))
| 'a$utruth'(liar(a)) ),
inference(resolution,[status(thm)],[d7,c24]) ).
cnf(d9,plain,
( ~ 'a$utruth'(normal(b))
| ~ 'a$utruth'(normal(a)) ),
inference(resolution,[status(thm)],[c23,c18]) ).
cnf(d10,plain,
( ~ 'a$utruth'(truthteller(b))
| ~ 'a$utruth'(normal(a)) ),
inference(resolution,[status(thm)],[c23,c17]) ).
cnf(d11,plain,
( ~ 'a$utruth'(normal(a))
| 'a$utruth'(normal(b))
| 'a$utruth'(liar(b)) ),
inference(resolution,[status(thm)],[c24,d10]) ).
cnf(d12,plain,
( 'a$utruth'(normal(b))
| ~ 'a$utruth'(normal(a)) ),
inference(resolution,[status(thm)],[d4,d11]) ).
cnf(d13,plain,
( 'a$utruth'(liar(a))
| 'a$utruth'(normal(b)) ),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( ~ 'a$utruth'(normal(a))
| 'a$utruth'(liar(a)) ),
inference(resolution,[status(thm)],[d13,d9]) ).
cnf(d15,plain,
( 'a$utruth'(liar(a))
| 'a$utruth'(liar(a)) ),
inference(resolution,[status(thm)],[d14,d8]) ).
cnf(d16,plain,
'a$utruth'(normal(b)),
inference(resolution,[status(thm)],[d15,d5]) ).
cnf(d17,plain,
( ~ 'a$utruth'(normal(b))
| ~ 'a$utruth'(liar(a)) ),
inference(resolution,[status(thm)],[c23,c21]) ).
cnf(d18,plain,
~ 'a$utruth'(normal(b)),
inference(resolution,[status(thm)],[d15,d17]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[d18,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ027-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n020.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 05:05:50 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.70/2.02 % SZS status Unsatisfiable for theBenchmark.p
% 10.70/2.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------