%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : PUZ018-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 08:22:04 AM UTC 2026
% Result : Unsatisfiable 14.20s 4.16s
% Output : CNFRefutation 14.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 23
% Syntax : Number of clauses : 87 ( 48 unt; 23 nHn; 79 RR)
% Number of literals : 192 ( 0 equ; 78 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 10 con; 0-0 aty)
% Number of variables : 44 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(all_on_a_on,axiom,
( on(a,X0)
| ~ 'all$uon'(X0) ) ).
cnf(all_on_b_on,axiom,
( on(b,X0)
| ~ 'all$uon'(X0) ) ).
cnf(all_on_c_on,axiom,
( on(c,X0)
| ~ 'all$uon'(X0) ) ).
cnf(monday_follows_sunday,axiom,
consecutive(sunday,monday) ).
cnf(tuesday_follows_monday,axiom,
consecutive(monday,tuesday) ).
cnf(wednesday_follows_tuesday,axiom,
consecutive(tuesday,wednesday) ).
cnf(thursday_follows_wednesday,axiom,
consecutive(wednesday,thursday) ).
cnf(friday_follows_thursday,axiom,
consecutive(thursday,friday) ).
cnf(a_not_b,axiom,
~ 'same$uperson'(a,b) ).
cnf(a_not_c,axiom,
~ 'same$uperson'(a,c) ).
cnf(sunday_not_tuesday,axiom,
~ 'same$uday'(sunday,tuesday) ).
cnf(sunday_not_thursday,axiom,
~ 'same$uday'(sunday,thursday) ).
cnf(tuesday_not_thursday,axiom,
~ 'same$uday'(tuesday,thursday) ).
cnf(all_on_one_day,hypothesis,
( 'all$uon'(saturday)
| 'all$uon'(friday)
| 'all$uon'(thursday)
| 'all$uon'(wednesday)
| 'all$uon'(tuesday)
| 'all$uon'(monday)
| 'all$uon'(sunday) ) ).
cnf(not_on_for_3_days,hypothesis,
( ~ on(X4,X2)
| ~ on(X4,X1)
| ~ on(X4,X0)
| ~ consecutive(X2,X3)
| ~ consecutive(X1,X2)
| ~ consecutive(X0,X1) ) ).
cnf(no_two_off_twice_together,hypothesis,
( 'same$uday'(X1,X2)
| 'same$uperson'(X0,X3)
| on(X3,X2)
| on(X3,X1)
| on(X0,X2)
| on(X0,X1) ) ).
cnf(a_off_sunday,hypothesis,
~ on(a,sunday) ).
cnf(a_off_tuesday,hypothesis,
~ on(a,tuesday) ).
cnf(a_off_thursday,hypothesis,
~ on(a,thursday) ).
cnf(b_off_thursday,hypothesis,
~ on(b,thursday) ).
cnf(b_off_saturday,hypothesis,
~ on(b,saturday) ).
cnf(c_off_sunday,hypothesis,
~ on(c,sunday) ).
cnf(prove_all_on_friday,negated_conjecture,
~ 'all$uon'(friday) ).
cnf(c0,plain,
( on(a,X0)
| ~ 'all$uon'(X0) ),
inference(clausification,[status(esa)],[all_on_a_on]) ).
cnf(c1,plain,
( on(b,X0)
| ~ 'all$uon'(X0) ),
inference(clausification,[status(esa)],[all_on_b_on]) ).
cnf(c2,plain,
( on(c,X0)
| ~ 'all$uon'(X0) ),
inference(clausification,[status(esa)],[all_on_c_on]) ).
cnf(c5,plain,
consecutive(sunday,monday),
inference(clausification,[status(esa)],[monday_follows_sunday]) ).
cnf(c6,plain,
consecutive(monday,tuesday),
inference(clausification,[status(esa)],[tuesday_follows_monday]) ).
cnf(c7,plain,
consecutive(tuesday,wednesday),
inference(clausification,[status(esa)],[wednesday_follows_tuesday]) ).
cnf(c8,plain,
consecutive(wednesday,thursday),
inference(clausification,[status(esa)],[thursday_follows_wednesday]) ).
cnf(c9,plain,
consecutive(thursday,friday),
inference(clausification,[status(esa)],[friday_follows_thursday]) ).
cnf(c13,plain,
~ 'same$uperson'(a,b),
inference(clausification,[status(esa)],[a_not_b]) ).
cnf(c14,plain,
~ 'same$uperson'(a,c),
inference(clausification,[status(esa)],[a_not_c]) ).
cnf(c18,plain,
~ 'same$uday'(sunday,tuesday),
inference(clausification,[status(esa)],[sunday_not_tuesday]) ).
cnf(c20,plain,
~ 'same$uday'(sunday,thursday),
inference(clausification,[status(esa)],[sunday_not_thursday]) ).
cnf(c29,plain,
~ 'same$uday'(tuesday,thursday),
inference(clausification,[status(esa)],[tuesday_not_thursday]) ).
cnf(c38,plain,
( 'all$uon'(friday)
| 'all$uon'(monday)
| 'all$uon'(thursday)
| 'all$uon'(wednesday)
| 'all$uon'(saturday)
| 'all$uon'(tuesday)
| 'all$uon'(sunday) ),
inference(clausification,[status(esa)],[all_on_one_day]) ).
cnf(c39,plain,
( ~ on(X2,X3)
| ~ on(X2,X1)
| ~ consecutive(X1,X3)
| ~ consecutive(X3,X4)
| ~ on(X2,X0)
| ~ consecutive(X0,X1) ),
inference(clausification,[status(esa)],[not_on_for_3_days]) ).
cnf(c40,plain,
( 'same$uperson'(X2,X0)
| on(X2,X3)
| on(X0,X3)
| 'same$uday'(X1,X3)
| on(X2,X1)
| on(X0,X1) ),
inference(clausification,[status(esa)],[no_two_off_twice_together]) ).
cnf(c41,plain,
~ on(a,sunday),
inference(clausification,[status(esa)],[a_off_sunday]) ).
cnf(c42,plain,
~ on(a,tuesday),
inference(clausification,[status(esa)],[a_off_tuesday]) ).
cnf(c43,plain,
~ on(a,thursday),
inference(clausification,[status(esa)],[a_off_thursday]) ).
cnf(c44,plain,
~ on(b,thursday),
inference(clausification,[status(esa)],[b_off_thursday]) ).
cnf(c45,plain,
~ on(b,saturday),
inference(clausification,[status(esa)],[b_off_saturday]) ).
cnf(c46,plain,
~ on(c,sunday),
inference(clausification,[status(esa)],[c_off_sunday]) ).
cnf(c47,plain,
~ 'all$uon'(friday),
inference(clausification,[status(esa)],[prove_all_on_friday]) ).
cnf(d0,plain,
( ~ consecutive(tuesday,X2)
| ~ consecutive(X1,monday)
| ~ on(X0,monday)
| ~ on(X0,tuesday)
| ~ on(X0,X1) ),
inference(resolution,[status(thm)],[c39,c6]) ).
cnf(d1,plain,
( ~ consecutive(X1,monday)
| ~ on(X0,tuesday)
| ~ on(X0,monday)
| ~ on(X0,X1) ),
inference(resolution,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
( ~ on(X0,tuesday)
| ~ on(X0,monday)
| ~ on(X0,sunday) ),
inference(resolution,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
( 'same$uperson'(X0,X1)
| on(X1,tuesday)
| on(X1,thursday)
| on(X0,tuesday)
| on(X0,thursday) ),
inference(resolution,[status(thm)],[c40,c29]) ).
cnf(d4,plain,
( on(a,thursday)
| on(a,tuesday)
| on(b,thursday)
| on(b,tuesday) ),
inference(resolution,[status(thm)],[d3,c13]) ).
cnf(d5,plain,
( on(b,thursday)
| on(b,tuesday)
| on(a,thursday) ),
inference(resolution,[status(thm)],[c42,d4]) ).
cnf(d6,plain,
( on(b,thursday)
| on(b,tuesday) ),
inference(resolution,[status(thm)],[c43,d5]) ).
cnf(d7,plain,
on(b,tuesday),
inference(resolution,[status(thm)],[c44,d6]) ).
cnf(d8,plain,
( ~ on(b,monday)
| ~ on(b,sunday) ),
inference(resolution,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
( 'same$uperson'(a,X1)
| 'same$uday'(sunday,X0)
| on(X1,sunday)
| on(X1,X0)
| on(a,X0) ),
inference(resolution,[status(thm)],[c40,c41]) ).
cnf(d10,plain,
( 'same$uperson'(a,b)
| 'same$uday'(sunday,thursday)
| on(a,thursday)
| on(b,sunday) ),
inference(resolution,[status(thm)],[d9,c44]) ).
cnf(d11,plain,
( 'same$uday'(sunday,thursday)
| on(b,sunday)
| on(a,thursday) ),
inference(resolution,[status(thm)],[c13,d10]) ).
cnf(d12,plain,
( on(b,sunday)
| on(a,thursday) ),
inference(resolution,[status(thm)],[c20,d11]) ).
cnf(d13,plain,
on(b,sunday),
inference(resolution,[status(thm)],[c43,d12]) ).
cnf(d14,plain,
~ on(b,monday),
inference(resolution,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
~ 'all$uon'(monday),
inference(resolution,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
( 'all$uon'(saturday)
| 'all$uon'(thursday)
| 'all$uon'(wednesday)
| 'all$uon'(tuesday)
| 'all$uon'(monday)
| 'all$uon'(sunday) ),
inference(resolution,[status(thm)],[c47,c38]) ).
cnf(d17,plain,
~ 'all$uon'(sunday),
inference(resolution,[status(thm)],[c41,c0]) ).
cnf(d18,plain,
( 'all$uon'(saturday)
| 'all$uon'(thursday)
| 'all$uon'(wednesday)
| 'all$uon'(tuesday)
| 'all$uon'(monday) ),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
~ 'all$uon'(tuesday),
inference(resolution,[status(thm)],[c42,c0]) ).
cnf(d20,plain,
( 'all$uon'(saturday)
| 'all$uon'(thursday)
| 'all$uon'(wednesday)
| 'all$uon'(monday) ),
inference(resolution,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
~ 'all$uon'(thursday),
inference(resolution,[status(thm)],[c43,c0]) ).
cnf(d22,plain,
( 'all$uon'(saturday)
| 'all$uon'(wednesday)
| 'all$uon'(monday) ),
inference(resolution,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
~ 'all$uon'(saturday),
inference(resolution,[status(thm)],[c45,c1]) ).
cnf(d24,plain,
( 'all$uon'(wednesday)
| 'all$uon'(monday) ),
inference(resolution,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
( 'same$uperson'(a,X0)
| 'same$uday'(sunday,thursday)
| on(X0,sunday)
| on(X0,thursday) ),
inference(resolution,[status(thm)],[d9,c43]) ).
cnf(d26,plain,
( 'same$uperson'(a,X0)
| on(X0,thursday)
| on(X0,sunday) ),
inference(resolution,[status(thm)],[c20,d25]) ).
cnf(d27,plain,
( on(c,thursday)
| on(c,sunday) ),
inference(resolution,[status(thm)],[d26,c14]) ).
cnf(d28,plain,
on(c,thursday),
inference(resolution,[status(thm)],[c46,d27]) ).
cnf(d29,plain,
( ~ consecutive(thursday,X2)
| ~ consecutive(X1,wednesday)
| ~ on(X0,wednesday)
| ~ on(X0,thursday)
| ~ on(X0,X1) ),
inference(resolution,[status(thm)],[c39,c8]) ).
cnf(d30,plain,
( ~ consecutive(X1,wednesday)
| ~ on(X0,thursday)
| ~ on(X0,wednesday)
| ~ on(X0,X1) ),
inference(resolution,[status(thm)],[d29,c9]) ).
cnf(d31,plain,
( ~ on(X0,thursday)
| ~ on(X0,wednesday)
| ~ on(X0,tuesday) ),
inference(resolution,[status(thm)],[d30,c7]) ).
cnf(d32,plain,
( ~ on(c,wednesday)
| ~ on(c,tuesday) ),
inference(resolution,[status(thm)],[d31,d28]) ).
cnf(d33,plain,
( 'same$uperson'(a,X0)
| 'same$uday'(sunday,tuesday)
| on(X0,sunday)
| on(X0,tuesday) ),
inference(resolution,[status(thm)],[d9,c42]) ).
cnf(d34,plain,
( 'same$uperson'(a,X0)
| on(X0,tuesday)
| on(X0,sunday) ),
inference(resolution,[status(thm)],[c18,d33]) ).
cnf(d35,plain,
( on(c,tuesday)
| on(c,sunday) ),
inference(resolution,[status(thm)],[d34,c14]) ).
cnf(d36,plain,
on(c,tuesday),
inference(resolution,[status(thm)],[c46,d35]) ).
cnf(d37,plain,
~ on(c,wednesday),
inference(resolution,[status(thm)],[d36,d32]) ).
cnf(d38,plain,
~ 'all$uon'(wednesday),
inference(resolution,[status(thm)],[d37,c2]) ).
cnf(d39,plain,
'all$uon'(monday),
inference(resolution,[status(thm)],[d38,d24]) ).
cnf(d40,plain,
$false,
inference(resolution,[status(thm)],[d39,d15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.25 % Problem : PUZ018-1 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.27 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.64 % Computer : n001.cluster.edu
% 0.18/0.64 % Model : x86_64 x86_64
% 0.18/0.64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.64 % Memory : 8046.5625MB
% 0.18/0.64 % OS : Linux 6.8.0-71-generic
% 0.18/0.64 % CPULimit : 300
% 0.18/0.64 % WCLimit : 300
% 0.18/0.64 % DateTime : Sat Sep 26 05:10:12 UTC 2026
% 0.18/0.65 % CPUTime :
% 0.18/0.65 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.20/4.16 % SZS status Unsatisfiable for theBenchmark.p
% 14.20/4.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------