%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL039-1 : 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 : n011.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 07:53:36 AM UTC 2026
% Result : Unsatisfiable 24.37s 3.60s
% Output : CNFRefutation 24.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of clauses : 47 ( 20 unt; 0 nHn; 30 RR)
% Number of literals : 85 ( 0 equ; 41 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 85 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(implies(X0,X1)) ) ).
cnf(cn_18,axiom,
'is$ua$utheorem'(implies(X0,implies(X1,X0))) ).
cnf(cn_35,axiom,
'is$ua$utheorem'(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))) ).
cnf(cn_49,axiom,
'is$ua$utheorem'(implies(implies(not(X0),not(X1)),implies(X1,X0))) ).
cnf(necessitation1,axiom,
'is$ua$utheorem'(implies(necessary(implies(X0,X1)),implies(necessary(X0),necessary(X1)))) ).
cnf(necessitation2,axiom,
'is$ua$utheorem'(implies(necessary(X0),X0)) ).
cnf(axiom_of_necessitation,axiom,
( 'is$ua$utheorem'(necessary(X0))
| ~ 'is$ua$utheorem'(X0) ) ).
cnf(prove_this,negated_conjecture,
~ 'is$ua$utheorem'(implies(necessary(a),not(necessary(not(a))))) ).
cnf(c0,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(clausification,[status(esa)],[condensed_detachment]) ).
cnf(c1,plain,
'is$ua$utheorem'(implies(X0,implies(X1,X0))),
inference(clausification,[status(esa)],[cn_18]) ).
cnf(c2,plain,
'is$ua$utheorem'(implies(implies(X0,implies(X1,X2)),implies(implies(X0,X1),implies(X0,X2)))),
inference(clausification,[status(esa)],[cn_35]) ).
cnf(c3,plain,
'is$ua$utheorem'(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(clausification,[status(esa)],[cn_49]) ).
cnf(c4,plain,
'is$ua$utheorem'(implies(necessary(implies(X0,X1)),implies(necessary(X0),necessary(X1)))),
inference(clausification,[status(esa)],[necessitation1]) ).
cnf(c5,plain,
'is$ua$utheorem'(implies(necessary(X0),X0)),
inference(clausification,[status(esa)],[necessitation2]) ).
cnf(c6,plain,
( 'is$ua$utheorem'(necessary(X0))
| ~ 'is$ua$utheorem'(X0) ),
inference(clausification,[status(esa)],[axiom_of_necessitation]) ).
cnf(c7,plain,
~ 'is$ua$utheorem'(implies(necessary(a),not(necessary(not(a))))),
inference(clausification,[status(esa)],[prove_this]) ).
cnf(d0,plain,
( ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
( ~ 'is$ua$utheorem'(implies(X0,implies(X1,X2)))
| 'is$ua$utheorem'(implies(implies(X0,X1),implies(X0,X2))) ),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d2,plain,
( ~ 'is$ua$utheorem'(implies(X0,X1))
| 'is$ua$utheorem'(implies(X0,X2))
| ~ 'is$ua$utheorem'(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
( ~ 'is$ua$utheorem'(implies(X2,X1))
| ~ 'is$ua$utheorem'(implies(X0,X2))
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( 'is$ua$utheorem'(implies(necessary(X0),X1))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
~ 'is$ua$utheorem'(implies(a,not(necessary(not(a))))),
inference(resolution,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
( ~ 'is$ua$utheorem'(implies(not(X1),not(X0)))
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d7,plain,
( ~ 'is$ua$utheorem'(necessary(implies(X0,X1)))
| 'is$ua$utheorem'(implies(necessary(X0),necessary(X1))) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d8,plain,
( ~ 'is$ua$utheorem'(necessary(X0))
| 'is$ua$utheorem'(necessary(X1))
| ~ 'is$ua$utheorem'(necessary(implies(X0,X1))) ),
inference(resolution,[status(thm)],[d7,c0]) ).
cnf(d9,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(necessary(X1))
| 'is$ua$utheorem'(necessary(X0)) ),
inference(resolution,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
( ~ 'is$ua$utheorem'(necessary(implies(X0,X1)))
| 'is$ua$utheorem'(necessary(necessary(X1)))
| ~ 'is$ua$utheorem'(necessary(necessary(X0))) ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(necessary(necessary(X1)))
| 'is$ua$utheorem'(necessary(necessary(X0))) ),
inference(resolution,[status(thm)],[d10,c6]) ).
cnf(d12,plain,
( ~ 'is$ua$utheorem'(necessary(X0))
| 'is$ua$utheorem'(necessary(necessary(X1)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d11,c6]) ).
cnf(d13,plain,
( 'is$ua$utheorem'(necessary(necessary(implies(X1,X0))))
| ~ 'is$ua$utheorem'(necessary(implies(not(X0),not(X1)))) ),
inference(resolution,[status(thm)],[d12,c3]) ).
cnf(d14,plain,
( ~ 'is$ua$utheorem'(implies(not(X1),not(X0)))
| 'is$ua$utheorem'(necessary(necessary(implies(X0,X1)))) ),
inference(resolution,[status(thm)],[d13,c6]) ).
cnf(d15,plain,
( ~ 'is$ua$utheorem'(implies(X0,X1))
| 'is$ua$utheorem'(implies(X0,X0)) ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d16,plain,
'is$ua$utheorem'(implies(X0,X0)),
inference(resolution,[status(thm)],[d15,c1]) ).
cnf(d17,plain,
'is$ua$utheorem'(necessary(necessary(implies(X0,X0)))),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
( ~ 'is$ua$utheorem'(necessary(X0))
| 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d19,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(necessary(necessary(X1)))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d18,d4]) ).
cnf(d20,plain,
( ~ 'is$ua$utheorem'(implies(implies(X1,X1),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
( ~ 'is$ua$utheorem'(implies(X0,implies(X0,X1)))
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d20,d1]) ).
cnf(d22,plain,
( 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d3,c1]) ).
cnf(d23,plain,
'is$ua$utheorem'(implies(not(X0),implies(X0,X1))),
inference(resolution,[status(thm)],[d22,c3]) ).
cnf(d24,plain,
( 'is$ua$utheorem'(implies(not(X0),X2))
| ~ 'is$ua$utheorem'(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d23,d3]) ).
cnf(d25,plain,
'is$ua$utheorem'(implies(not(not(X0)),implies(X1,X0))),
inference(resolution,[status(thm)],[d24,c3]) ).
cnf(d26,plain,
'is$ua$utheorem'(implies(not(not(X0)),X0)),
inference(resolution,[status(thm)],[d25,d21]) ).
cnf(d27,plain,
( 'is$ua$utheorem'(implies(not(not(X0)),X1))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d26,d3]) ).
cnf(d28,plain,
( 'is$ua$utheorem'(implies(X1,not(X0)))
| ~ 'is$ua$utheorem'(implies(X0,not(X1))) ),
inference(resolution,[status(thm)],[d27,d6]) ).
cnf(d29,plain,
'is$ua$utheorem'(implies(X0,not(necessary(not(X0))))),
inference(resolution,[status(thm)],[d28,c5]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[d29,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n011.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 : Fri Sep 25 21:45:28 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.37/3.60 % SZS status Unsatisfiable for theBenchmark.p
% 24.37/3.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------