%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : PUZ032-1 : 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 : n006.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 08:22:08 AM UTC 2026
% Result : Unsatisfiable 9.69s 1.68s
% Output : CNFRefutation 9.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 12 unt; 6 nHn; 26 RR)
% Number of literals : 53 ( 0 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_says_a_says_hes_a_liar,hypothesis,
'a$utruth'(says(b,says(a,liar(a)))) ).
cnf(c_says_b_is_a_liar,hypothesis,
'a$utruth'(says(c,liar(b))) ).
cnf(prove_c_is_a_truthteller,negated_conjecture,
~ 'a$utruth'(truthteller(c)) ).
cnf(truthteller_or_liar,axiom,
( 'a$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$utruth'(liar(X0)) ) ).
cnf(truths_are_told_by_truthtellers,axiom,
( 'a$utruth'(truthteller(X1))
| ~ 'a$utruth'(says(X1,X0))
| ~ 'a$utruth'(X0) ) ).
cnf(liars_are_told_by_liars,axiom,
( 'a$utruth'(liar(X1))
| ~ 'a$utruth'(says(X1,X0))
| 'a$utruth'(X0) ) ).
cnf(c1,plain,
'a$utruth'(says(b,says(a,liar(a)))),
inference(clausification,[status(esa)],[b_says_a_says_hes_a_liar]) ).
cnf(c2,plain,
'a$utruth'(says(c,liar(b))),
inference(clausification,[status(esa)],[c_says_b_is_a_liar]) ).
cnf(c3,plain,
~ 'a$utruth'(truthteller(c)),
inference(clausification,[status(esa)],[prove_c_is_a_truthteller]) ).
cnf(c4,plain,
( 'a$utruth'(liar(X0))
| 'a$utruth'(truthteller(X0)) ),
inference(clausification,[status(esa)],[truthteller_or_liar]) ).
cnf(c6,plain,
( 'a$utruth'(X1)
| ~ 'a$utruth'(says(X0,X1))
| ~ 'a$utruth'(truthteller(X0)) ),
inference(clausification,[status(esa)],[truthtellers_tell_truth]) ).
cnf(c7,plain,
( ~ 'a$utruth'(X1)
| ~ 'a$utruth'(says(X0,X1))
| ~ 'a$utruth'(liar(X0)) ),
inference(clausification,[status(esa)],[liars_lie]) ).
cnf(c8,plain,
( 'a$utruth'(truthteller(X1))
| ~ 'a$utruth'(says(X1,X0))
| ~ 'a$utruth'(X0) ),
inference(clausification,[status(esa)],[truths_are_told_by_truthtellers]) ).
cnf(c9,plain,
( 'a$utruth'(liar(X1))
| ~ 'a$utruth'(says(X1,X0))
| 'a$utruth'(X0) ),
inference(clausification,[status(esa)],[liars_are_told_by_liars]) ).
cnf(d0,plain,
( ~ 'a$utruth'(truthteller(b))
| 'a$utruth'(says(a,liar(a))) ),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d1,plain,
( 'a$utruth'(liar(a))
| 'a$utruth'(liar(a))
| ~ 'a$utruth'(truthteller(b)) ),
inference(resolution,[status(thm)],[d0,c9]) ).
cnf(d2,plain,
( 'a$utruth'(truthteller(b))
| ~ 'a$utruth'(says(a,liar(a))) ),
inference(resolution,[status(thm)],[c8,c1]) ).
cnf(d3,plain,
( 'a$utruth'(liar(b))
| 'a$utruth'(says(a,liar(a))) ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d4,plain,
( ~ 'a$utruth'(liar(c))
| ~ 'a$utruth'(liar(b)) ),
inference(resolution,[status(thm)],[c7,c2]) ).
cnf(d5,plain,
'a$utruth'(liar(c)),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(d6,plain,
~ 'a$utruth'(liar(b)),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
'a$utruth'(says(a,liar(a))),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
'a$utruth'(truthteller(b)),
inference(resolution,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
'a$utruth'(liar(a)),
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
( ~ 'a$utruth'(liar(a))
| ~ 'a$utruth'(liar(a)) ),
inference(resolution,[status(thm)],[d7,c7]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ032-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 05:06:11 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.69/1.68 % SZS status Unsatisfiable for theBenchmark.p
% 9.69/1.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------