%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL166-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 07:53:54 AM UTC 2026
% Result : Unsatisfiable 105.90s 27.26s
% Output : CNFRefutation 105.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 3
% Syntax : Number of clauses : 60 ( 10 unt; 0 nHn; 46 RR)
% Number of literals : 153 ( 0 equ; 95 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 7 ( 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 : 176 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(equivalent(X0,X1)) ) ).
cnf(xhn,axiom,
'is$ua$utheorem'(equivalent(X0,equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1)))) ).
cnf(prove_um,negated_conjecture,
~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))) ).
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(X1,X2),equivalent(equivalent(X2,X0),X1)))),
inference(clausification,[status(esa)],[xhn]) ).
cnf(c2,plain,
~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(a,b),c),equivalent(b,equivalent(c,a)))),
inference(clausification,[status(esa)],[prove_um]) ).
cnf(d0,plain,
( ~ 'is$ua$utheorem'(X2)
| 'is$ua$utheorem'(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X0))) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
( ~ 'is$ua$utheorem'(equivalent(X2,X1))
| 'is$ua$utheorem'(equivalent(equivalent(X1,X0),X2))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( ~ 'is$ua$utheorem'(equivalent(X2,X0))
| 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(equivalent(X1,X2))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X0),X2)),X1))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d4,plain,
( ~ 'is$ua$utheorem'(equivalent(X0,equivalent(X3,X2)))
| ~ 'is$ua$utheorem'(equivalent(equivalent(X2,X1),X3))
| 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(equivalent(X1,equivalent(equivalent(equivalent(X0,X2),X3),X3)))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(equivalent(X1,equivalent(X2,X0)))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(X1,X2),X0))
| ~ 'is$ua$utheorem'(X2)
| 'is$ua$utheorem'(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
( 'is$ua$utheorem'(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,equivalent(X3,X0)),X1)),X3))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
( ~ 'is$ua$utheorem'(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),equivalent(equivalent(X3,equivalent(X4,X0)),X2)),X4)))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d4,c1]) ).
cnf(d10,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(X2,equivalent(X0,X3)),X1))
| 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(equivalent(X0,equivalent(X1,X2))) ),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
( ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X2,equivalent(X0,X1))))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( 'is$ua$utheorem'(equivalent(X1,equivalent(X2,equivalent(equivalent(X2,X1),X0))))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d11,c1]) ).
cnf(d13,plain,
( 'is$ua$utheorem'(X4)
| ~ 'is$ua$utheorem'(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X4),X2))),X0))) ),
inference(resolution,[status(thm)],[d3,c1]) ).
cnf(d14,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X0),X1)))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d13,d0]) ).
cnf(d15,plain,
( 'is$ua$utheorem'(equivalent(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d8,d3]) ).
cnf(d16,plain,
( 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(equivalent(equivalent(X1,X2),X0))
| ~ 'is$ua$utheorem'(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
( ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(equivalent(X1,equivalent(X3,X0)))
| 'is$ua$utheorem'(equivalent(equivalent(X0,equivalent(X1,X2)),X3)) ),
inference(resolution,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
( ~ 'is$ua$utheorem'(X3)
| ~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(X1,X3),X0),X2))
| ~ 'is$ua$utheorem'(X2)
| 'is$ua$utheorem'(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d19,plain,
( ~ 'is$ua$utheorem'(X2)
| 'is$ua$utheorem'(equivalent(X1,X3))
| ~ 'is$ua$utheorem'(equivalent(equivalent(X1,X2),equivalent(X3,X0)))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d18,d0]) ).
cnf(d20,plain,
( ~ 'is$ua$utheorem'(X2)
| 'is$ua$utheorem'(equivalent(X1,equivalent(X0,X2)))
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d19,d0]) ).
cnf(d21,plain,
( 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(equivalent(X1,X2))
| ~ 'is$ua$utheorem'(equivalent(X0,X1))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d20,d14]) ).
cnf(d22,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(X2,X3),equivalent(equivalent(X3,X1),X2)),X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d21,c1]) ).
cnf(d23,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(equivalent(X1,X0))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d8,d22]) ).
cnf(d24,plain,
( ~ 'is$ua$utheorem'(equivalent(X2,equivalent(equivalent(X2,X1),X0)))
| 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d12,d23]) ).
cnf(d25,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(X0,X1),X1))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d24,c1]) ).
cnf(d26,plain,
( ~ 'is$ua$utheorem'(equivalent(X2,equivalent(equivalent(X2,X1),X0)))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d25,d17]) ).
cnf(d27,plain,
( ~ 'is$ua$utheorem'(X2)
| 'is$ua$utheorem'(equivalent(equivalent(equivalent(X1,X0),X1),X2))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d26,d12]) ).
cnf(d28,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(equivalent(equivalent(X0,X1),equivalent(X0,X2))) ),
inference(resolution,[status(thm)],[d27,d14]) ).
cnf(d29,plain,
( ~ 'is$ua$utheorem'(X2)
| 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(equivalent(equivalent(X0,equivalent(X0,X1)),X2)) ),
inference(resolution,[status(thm)],[d28,d12]) ).
cnf(d30,plain,
( ~ 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(X1,X0),X1),X2))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d24,d12]) ).
cnf(d31,plain,
( ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(equivalent(equivalent(X0,X1),equivalent(X0,X2))) ),
inference(resolution,[status(thm)],[d30,d0]) ).
cnf(d32,plain,
( ~ 'is$ua$utheorem'(X2)
| 'is$ua$utheorem'(equivalent(equivalent(X0,equivalent(equivalent(X1,X0),X2)),X1)) ),
inference(resolution,[status(thm)],[d31,c1]) ).
cnf(d33,plain,
( ~ 'is$ua$utheorem'(equivalent(X2,equivalent(equivalent(X1,X2),X0)))
| 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d32,c0]) ).
cnf(d34,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(X1,X1),X0))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d33,c1]) ).
cnf(d35,plain,
'is$ua$utheorem'(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,equivalent(X2,X2)),X0))),
inference(resolution,[status(thm)],[d34,c1]) ).
cnf(d36,plain,
'is$ua$utheorem'(equivalent(X0,X0)),
inference(resolution,[status(thm)],[d35,d14]) ).
cnf(d37,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(equivalent(X0,equivalent(X0,X1))) ),
inference(resolution,[status(thm)],[d36,d29]) ).
cnf(d38,plain,
'is$ua$utheorem'(equivalent(equivalent(X0,equivalent(X1,X0)),X1)),
inference(resolution,[status(thm)],[d37,c1]) ).
cnf(d39,plain,
( ~ 'is$ua$utheorem'(equivalent(X1,equivalent(X0,X1)))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d38,c0]) ).
cnf(d40,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,equivalent(X3,X0)),X1)),X3))
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d16,c1]) ).
cnf(d41,plain,
( 'is$ua$utheorem'(equivalent(X2,equivalent(X3,X1)))
| ~ 'is$ua$utheorem'(equivalent(equivalent(X1,equivalent(X2,X0)),X3))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d19,c1]) ).
cnf(d42,plain,
( 'is$ua$utheorem'(equivalent(equivalent(X2,equivalent(X3,X0)),equivalent(X3,equivalent(X1,X2))))
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d8,d41]) ).
cnf(d43,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(X1,equivalent(X2,X2)),X0))
| 'is$ua$utheorem'(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[d35,d23]) ).
cnf(d44,plain,
( ~ 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(equivalent(equivalent(X0,equivalent(X1,X2)),X2)) ),
inference(resolution,[status(thm)],[d43,d42]) ).
cnf(d45,plain,
( 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(equivalent(X1,X0))
| ~ 'is$ua$utheorem'(equivalent(X0,equivalent(X1,X2))) ),
inference(resolution,[status(thm)],[d44,d40]) ).
cnf(d46,plain,
( ~ 'is$ua$utheorem'(equivalent(equivalent(X2,X0),X1))
| 'is$ua$utheorem'(equivalent(equivalent(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d45,c1]) ).
cnf(d47,plain,
( ~ 'is$ua$utheorem'(equivalent(X1,X2))
| ~ 'is$ua$utheorem'(X0)
| 'is$ua$utheorem'(equivalent(equivalent(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d46,d1]) ).
cnf(d48,plain,
( 'is$ua$utheorem'(X2)
| ~ 'is$ua$utheorem'(equivalent(X1,equivalent(X2,equivalent(X0,X1))))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d47,d39]) ).
cnf(d49,plain,
( ~ 'is$ua$utheorem'(equivalent(X1,X0))
| 'is$ua$utheorem'(equivalent(X0,X1)) ),
inference(resolution,[status(thm)],[d48,c1]) ).
cnf(d50,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(X0,X1),equivalent(equivalent(X1,X2),X0)),X2)),
inference(resolution,[status(thm)],[d49,c1]) ).
cnf(d51,plain,
( 'is$ua$utheorem'(equivalent(X1,equivalent(X2,X0)))
| ~ 'is$ua$utheorem'(equivalent(equivalent(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d50,d7]) ).
cnf(d52,plain,
'is$ua$utheorem'(equivalent(equivalent(equivalent(X0,X1),X2),equivalent(X1,equivalent(X2,X0)))),
inference(resolution,[status(thm)],[d51,d50]) ).
cnf(d53,plain,
$false,
inference(resolution,[status(thm)],[d52,c2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL166-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n015.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 21:59:43 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 105.90/27.26 % SZS status Unsatisfiable for theBenchmark.p
% 105.90/27.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------