%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL126-1 : 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 : n016.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 07:53:49 AM UTC 2026
% Result : Unsatisfiable 12.86s 2.41s
% Output : CNFRefutation 12.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of clauses : 17 ( 9 unt; 0 nHn; 8 RR)
% Number of literals : 30 ( 0 equ; 16 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; 3 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(equivalent(X0,X1)) ) ).
cnf(q_3,axiom,
'is$ua$utheorem'(equivalent(X0,equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,X1)))) ).
cnf(q_4,axiom,
'is$ua$utheorem'(equivalent(equivalent(X0,X1),equivalent(equivalent(X0,X2),equivalent(X1,X2)))) ).
cnf(prove_q_2,negated_conjecture,
~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))) ).
cnf(c0,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(equivalent(X0,X1)) ),
inference(clausification,[status(esa)],[condensed_detachment]) ).
cnf(c1,plain,
'is$ua$utheorem'(equivalent(X0,equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,X1)))),
inference(clausification,[status(esa)],[q_3]) ).
cnf(c2,plain,
'is$ua$utheorem'(equivalent(equivalent(X0,X1),equivalent(equivalent(X0,X2),equivalent(X1,X2)))),
inference(clausification,[status(esa)],[q_4]) ).
cnf(c3,plain,
~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(a,b),equivalent(c,b)),equivalent(a,c))),
inference(clausification,[status(esa)],[prove_q_2]) ).
cnf(d0,plain,
( ~ 'is$ua$utheorem'(equivalent(X0,X2))
| 'is$ua$utheorem'(equivalent(equivalent(X0,X1),equivalent(X2,X1))) ),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
( ~ 'is$ua$utheorem'(equivalent(X0,X2))
| 'is$ua$utheorem'(equivalent(X1,X2))
| ~ 'is$ua$utheorem'(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(X0,X2),X3))
| 'is$ua$utheorem'(equivalent(equivalent(equivalent(X0,X1),equivalent(X2,X1)),X3)) ),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
~ 'is$ua$utheorem'(equivalent(equivalent(a,c),equivalent(a,c))),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( ~ 'is$ua$utheorem'(X0)
| 'is$ua$utheorem'(equivalent(equivalent(X0,equivalent(X1,X2)),equivalent(X2,X1))) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d5,plain,
( ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(equivalent(equivalent(X3,equivalent(X1,X0)),X2))
| 'is$ua$utheorem'(equivalent(equivalent(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d1,d4]) ).
cnf(d6,plain,
( ~ 'is$ua$utheorem'(X0)
| 'is$ua$utheorem'(equivalent(equivalent(X1,X2),equivalent(X1,X2)))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
'is$ua$utheorem'(equivalent(equivalent(X0,X1),equivalent(X0,X1))),
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL126-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n016.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Fri Sep 25 21:58:15 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.86/2.41 % SZS status Unsatisfiable for theBenchmark.p
% 12.86/2.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------