%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL372-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 07:54:25 AM UTC 2026
% Result : Unsatisfiable 15.03s 13.96s
% Output : CNFRefutation 15.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of clauses : 56 ( 29 unt; 0 nHn; 22 RR)
% Number of literals : 89 ( 0 equ; 39 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 126 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(implies(X0,X1)) ) ).
cnf(cn_1,axiom,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ).
cnf(cn_2,axiom,
'is$ua$utheorem'(implies(implies(not(X0),X0),X0)) ).
cnf(cn_3,axiom,
'is$ua$utheorem'(implies(X0,implies(not(X0),X1))) ).
cnf(prove_cn_28,negated_conjecture,
~ 'is$ua$utheorem'(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z))) ).
cnf(c0,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0) ),
inference(clausification,[status(esa)],[condensed_detachment]) ).
cnf(c1,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(clausification,[status(esa)],[cn_1]) ).
cnf(c2,plain,
'is$ua$utheorem'(implies(implies(not(X0),X0),X0)),
inference(clausification,[status(esa)],[cn_2]) ).
cnf(c3,plain,
'is$ua$utheorem'(implies(X0,implies(not(X0),X1))),
inference(clausification,[status(esa)],[cn_3]) ).
cnf(c4,plain,
~ 'is$ua$utheorem'(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z))),
inference(clausification,[status(esa)],[prove_cn_28]) ).
cnf(d0,plain,
( ~ 'is$ua$utheorem'(implies(X2,X0))
| 'is$ua$utheorem'(implies(implies(X0,X1),implies(X2,X1))) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
( ~ 'is$ua$utheorem'(implies(X1,X2))
| 'is$ua$utheorem'(implies(X0,X2))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( 'is$ua$utheorem'(implies(X0,X2))
| ~ 'is$ua$utheorem'(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( ~ 'is$ua$utheorem'(implies(X1,not(X0)))
| 'is$ua$utheorem'(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( ~ 'is$ua$utheorem'(implies(X0,X3))
| 'is$ua$utheorem'(implies(implies(X3,X1),X2))
| ~ 'is$ua$utheorem'(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d5,plain,
( 'is$ua$utheorem'(implies(implies(X1,X0),X0))
| ~ 'is$ua$utheorem'(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
~ 'is$ua$utheorem'(implies(implies(implies(y,u),x),implies(implies(x,y),y))),
inference(resolution,[status(thm)],[c4,d0]) ).
cnf(d7,plain,
( 'is$ua$utheorem'(implies(implies(X2,X0),X3))
| ~ 'is$ua$utheorem'(implies(implies(implies(X0,X1),implies(X2,X1)),X3)) ),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d8,plain,
( ~ 'is$ua$utheorem'(X0)
| 'is$ua$utheorem'(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d9,plain,
( 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(implies(not(X0),not(X1))) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d10,plain,
( ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( 'is$ua$utheorem'(implies(implies(X0,X2),implies(X0,X1)))
| ~ 'is$ua$utheorem'(implies(not(implies(X0,X1)),implies(X2,X1))) ),
inference(resolution,[status(thm)],[d5,d7]) ).
cnf(d12,plain,
( ~ 'is$ua$utheorem'(implies(X1,X2))
| 'is$ua$utheorem'(implies(implies(X0,X1),implies(X0,X2))) ),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( 'is$ua$utheorem'(implies(implies(X0,X3),implies(implies(X3,X1),X2)))
| ~ 'is$ua$utheorem'(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d12,d7]) ).
cnf(d14,plain,
~ 'is$ua$utheorem'(implies(implies(implies(y,u),y),y)),
inference(resolution,[status(thm)],[d13,d6]) ).
cnf(d15,plain,
~ 'is$ua$utheorem'(implies(not(y),implies(y,u))),
inference(resolution,[status(thm)],[d14,d5]) ).
cnf(d16,plain,
~ 'is$ua$utheorem'(implies(y,not(not(y)))),
inference(resolution,[status(thm)],[d15,d3]) ).
cnf(d17,plain,
'is$ua$utheorem'(implies(X0,implies(not(implies(not(X0),X1)),X2))),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d18,plain,
( 'is$ua$utheorem'(implies(X0,X3))
| ~ 'is$ua$utheorem'(implies(implies(not(implies(not(X0),X1)),X2),X3)) ),
inference(resolution,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
( ~ 'is$ua$utheorem'(implies(not(X1),not(implies(not(X0),X2))))
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d18,d5]) ).
cnf(d20,plain,
'is$ua$utheorem'(implies(implies(X0,not(not(implies(X0,X1)))),implies(X0,X1))),
inference(resolution,[status(thm)],[d11,c3]) ).
cnf(d21,plain,
'is$ua$utheorem'(implies(X0,implies(implies(X1,X2),implies(not(X0),X2)))),
inference(resolution,[status(thm)],[d2,c1]) ).
cnf(d22,plain,
( 'is$ua$utheorem'(implies(X2,X3))
| ~ 'is$ua$utheorem'(implies(implies(implies(X0,X1),implies(not(X2),X1)),X3)) ),
inference(resolution,[status(thm)],[d21,d1]) ).
cnf(d23,plain,
( ~ 'is$ua$utheorem'(implies(X1,implies(X3,X2)))
| 'is$ua$utheorem'(implies(X0,implies(X1,implies(not(X0),X2)))) ),
inference(resolution,[status(thm)],[d22,d0]) ).
cnf(d24,plain,
'is$ua$utheorem'(implies(X0,implies(X1,implies(not(X0),X2)))),
inference(resolution,[status(thm)],[d23,d17]) ).
cnf(d25,plain,
( 'is$ua$utheorem'(implies(X1,X3))
| ~ 'is$ua$utheorem'(implies(implies(X0,implies(not(X1),X2)),X3)) ),
inference(resolution,[status(thm)],[d24,d1]) ).
cnf(d26,plain,
'is$ua$utheorem'(implies(X0,X0)),
inference(resolution,[status(thm)],[d2,c2]) ).
cnf(d27,plain,
( ~ 'is$ua$utheorem'(implies(X3,X0))
| 'is$ua$utheorem'(implies(implies(X1,X2),implies(X3,X2)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d28,plain,
( 'is$ua$utheorem'(implies(implies(X1,X2),implies(X0,X2)))
| ~ 'is$ua$utheorem'(implies(X0,implies(not(X1),X1))) ),
inference(resolution,[status(thm)],[d27,c2]) ).
cnf(d29,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(resolution,[status(thm)],[d28,d26]) ).
cnf(d30,plain,
( 'is$ua$utheorem'(implies(X2,X1))
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d31,plain,
'is$ua$utheorem'(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[d28,d17]) ).
cnf(d32,plain,
( 'is$ua$utheorem'(implies(X3,implies(X0,X2)))
| ~ 'is$ua$utheorem'(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[d31,d30]) ).
cnf(d33,plain,
'is$ua$utheorem'(implies(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[d32,c2]) ).
cnf(d34,plain,
( 'is$ua$utheorem'(implies(X2,X1))
| ~ 'is$ua$utheorem'(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[d33,d1]) ).
cnf(d35,plain,
'is$ua$utheorem'(implies(X0,implies(implies(not(X1),X1),X1))),
inference(resolution,[status(thm)],[d34,d29]) ).
cnf(d36,plain,
'is$ua$utheorem'(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[d35,d11]) ).
cnf(d37,plain,
'is$ua$utheorem'(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[d36,d25]) ).
cnf(d38,plain,
( 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d37,d1]) ).
cnf(d39,plain,
'is$ua$utheorem'(implies(not(not(implies(X0,X1))),implies(X0,X1))),
inference(resolution,[status(thm)],[d38,d20]) ).
cnf(d40,plain,
( ~ 'is$ua$utheorem'(implies(X0,implies(not(X1),X1)))
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d36,c0]) ).
cnf(d41,plain,
'is$ua$utheorem'(implies(not(not(implies(not(X0),X0))),X0)),
inference(resolution,[status(thm)],[d40,d39]) ).
cnf(d42,plain,
'is$ua$utheorem'(implies(X0,not(implies(not(not(X0)),not(X0))))),
inference(resolution,[status(thm)],[d41,d9]) ).
cnf(d43,plain,
'is$ua$utheorem'(implies(not(not(X0)),X0)),
inference(resolution,[status(thm)],[d42,d19]) ).
cnf(d44,plain,
'is$ua$utheorem'(implies(X0,not(not(X0)))),
inference(resolution,[status(thm)],[d43,d9]) ).
cnf(d45,plain,
$false,
inference(resolution,[status(thm)],[d44,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL372-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 22:20:44 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.03/13.96 % SZS status Unsatisfiable for theBenchmark.p
% 15.03/13.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------