%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL123-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 07:53:49 AM UTC 2026
% Result : Unsatisfiable 103.97s 40.38s
% Output : CNFRefutation 103.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of clauses : 33 ( 6 unt; 0 nHn; 24 RR)
% Number of literals : 156 ( 0 equ; 138 neg)
% Maximal clause size : 12 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 181 ( 115 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(equivalent(X0,X1)) ) ).
cnf(lg_2,axiom,
'is$ua$utheorem'(equivalent(X0,equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))))) ).
cnf(prove_lg_4,negated_conjecture,
~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(e,equivalent(b,f))),equivalent(a,equivalent(e,equivalent(c,f))))) ).
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(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))))),
inference(clausification,[status(esa)],[lg_2]) ).
cnf(c2,plain,
~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(e,equivalent(b,f))),equivalent(a,equivalent(e,equivalent(c,f))))),
inference(clausification,[status(esa)],[prove_lg_4]) ).
cnf(d0,plain,
( ~ 'is$ua$utheorem'(X0)
| 'is$ua$utheorem'(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3))))) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
( ~ 'is$ua$utheorem'(X0)
| 'is$ua$utheorem'(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3))))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( ~ 'is$ua$utheorem'(equivalent(X1,X3))
| 'is$ua$utheorem'(equivalent(equivalent(X1,X2),equivalent(X3,X2)))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
( ~ 'is$ua$utheorem'(equivalent(X1,X3))
| 'is$ua$utheorem'(equivalent(X2,X3))
| ~ 'is$ua$utheorem'(equivalent(X1,X2))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
( ~ 'is$ua$utheorem'(X5)
| ~ 'is$ua$utheorem'(equivalent(equivalent(X1,X3),X4))
| 'is$ua$utheorem'(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X4))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(X2,X5),equivalent(X3,X5)))
| 'is$ua$utheorem'(X4)
| ~ 'is$ua$utheorem'(equivalent(equivalent(X2,X3),X4))
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
( ~ 'is$ua$utheorem'(equivalent(X3,equivalent(equivalent(X4,X6),equivalent(X5,X6))))
| ~ 'is$ua$utheorem'(equivalent(equivalent(X3,equivalent(X4,X5)),X0))
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
( ~ 'is$ua$utheorem'(X5)
| ~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(X3,X4),equivalent(X3,X4)),X2))
| 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(X3,equivalent(equivalent(X4,X5),equivalent(X6,X5))),equivalent(X3,equivalent(X4,X6))),X2))
| 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d9,plain,
( ~ 'is$ua$utheorem'(X7)
| ~ 'is$ua$utheorem'(X6)
| ~ 'is$ua$utheorem'(X5)
| 'is$ua$utheorem'(equivalent(equivalent(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(X3,X2))),X4),equivalent(equivalent(X0,equivalent(X1,X3)),X4))) ),
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
( ~ 'is$ua$utheorem'(X9)
| ~ 'is$ua$utheorem'(X8)
| 'is$ua$utheorem'(equivalent(equivalent(X4,equivalent(X5,X6)),equivalent(X4,equivalent(equivalent(X5,X7),equivalent(X6,X7)))))
| ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
( ~ 'is$ua$utheorem'(equivalent(X3,equivalent(X6,X5)))
| ~ 'is$ua$utheorem'(X7)
| ~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(X3,equivalent(X4,X5)),equivalent(X6,X4)),X2))
| 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d12,plain,
( ~ 'is$ua$utheorem'(equivalent(X4,equivalent(X7,equivalent(X6,X8))))
| ~ 'is$ua$utheorem'(X10)
| ~ 'is$ua$utheorem'(X9)
| 'is$ua$utheorem'(equivalent(equivalent(X4,equivalent(X5,X6)),equivalent(X7,equivalent(X5,X8))))
| ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d9,d11]) ).
cnf(d13,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(a,equivalent(b,c)),equivalent(a,equivalent(equivalent(b,f),equivalent(c,f)))))
| ~ 'is$ua$utheorem'(X5)
| ~ 'is$ua$utheorem'(X4)
| ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d12,c2]) ).
cnf(d14,plain,
( ~ 'is$ua$utheorem'(X11)
| ~ 'is$ua$utheorem'(X10)
| ~ 'is$ua$utheorem'(X9)
| ~ 'is$ua$utheorem'(X8)
| ~ 'is$ua$utheorem'(X7)
| ~ 'is$ua$utheorem'(X6)
| ~ 'is$ua$utheorem'(X5)
| ~ 'is$ua$utheorem'(X4)
| ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
( ~ 'is$ua$utheorem'(X10)
| ~ 'is$ua$utheorem'(X9)
| ~ 'is$ua$utheorem'(X8)
| ~ 'is$ua$utheorem'(X7)
| ~ 'is$ua$utheorem'(X6)
| ~ 'is$ua$utheorem'(X5)
| ~ 'is$ua$utheorem'(X4)
| ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d14,c1]) ).
cnf(d16,plain,
( ~ 'is$ua$utheorem'(X9)
| ~ 'is$ua$utheorem'(X8)
| ~ 'is$ua$utheorem'(X7)
| ~ 'is$ua$utheorem'(X6)
| ~ 'is$ua$utheorem'(X5)
| ~ 'is$ua$utheorem'(X4)
| ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d15,c1]) ).
cnf(d17,plain,
( ~ 'is$ua$utheorem'(X8)
| ~ 'is$ua$utheorem'(X7)
| ~ 'is$ua$utheorem'(X6)
| ~ 'is$ua$utheorem'(X5)
| ~ 'is$ua$utheorem'(X4)
| ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d16,c1]) ).
cnf(d18,plain,
( ~ 'is$ua$utheorem'(X7)
| ~ 'is$ua$utheorem'(X6)
| ~ 'is$ua$utheorem'(X5)
| ~ 'is$ua$utheorem'(X4)
| ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d17,c1]) ).
cnf(d19,plain,
( ~ 'is$ua$utheorem'(X6)
| ~ 'is$ua$utheorem'(X5)
| ~ 'is$ua$utheorem'(X4)
| ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d18,c1]) ).
cnf(d20,plain,
( ~ 'is$ua$utheorem'(X5)
| ~ 'is$ua$utheorem'(X4)
| ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d19,c1]) ).
cnf(d21,plain,
( ~ 'is$ua$utheorem'(X4)
| ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d20,c1]) ).
cnf(d22,plain,
( ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d21,c1]) ).
cnf(d23,plain,
( ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d22,c1]) ).
cnf(d24,plain,
( ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d23,c1]) ).
cnf(d25,plain,
~ 'is$ua$utheorem'(X0),
inference(resolution,[status(thm)],[d24,c1]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[d25,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL123-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 21:54:20 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 103.97/40.38 % SZS status Unsatisfiable for theBenchmark.p
% 103.97/40.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------