%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL372+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 07:54:25 AM UTC 2026
% Result : Theorem 109.68s 27.44s
% Output : CNFRefutation 109.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 66 ( 32 unt; 0 def)
% Number of atoms : 110 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 90 ( 46 ~; 42 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 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 : 154 ( 29 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [X0,X1] :
( ( 'is$ua$utheorem'(X0)
& 'is$ua$utheorem'(implies(X0,X1)) )
=> 'is$ua$utheorem'(X1) ) ).
fof(cn_1,axiom,
! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ).
fof(cn_2,axiom,
! [X0] : 'is$ua$utheorem'(implies(implies(not(X0),X0),X0)) ).
fof(cn_3,axiom,
! [X0,X1] : 'is$ua$utheorem'(implies(X0,implies(not(X0),X1))) ).
fof(prove_cn_28,conjecture,
'is$ua$utheorem'(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z))) ).
fof(negated_conjecture,negated_conjecture,
~ 'is$ua$utheorem'(implies(implies(implies(implies(x,y),y),z),implies(implies(implies(y,u),x),z))),
inference(negate_conjecture,[status(cth)],[prove_cn_28]) ).
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)],[negated_conjecture]) ).
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(implies(implies(y,u),x),implies(implies(x,y),y))),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,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(d3,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)],[d2,c1]) ).
cnf(d4,plain,
( ~ 'is$ua$utheorem'(X0)
| 'is$ua$utheorem'(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d5,plain,
( 'is$ua$utheorem'(implies(X0,X2))
| ~ 'is$ua$utheorem'(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d6,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)],[d2,d0]) ).
cnf(d7,plain,
( 'is$ua$utheorem'(implies(implies(X1,X0),X0))
| ~ 'is$ua$utheorem'(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
( 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(implies(not(X0),not(X1))) ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,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)],[d7,d3]) ).
cnf(d11,plain,
( ~ 'is$ua$utheorem'(implies(X1,X2))
| 'is$ua$utheorem'(implies(implies(X0,X1),implies(X0,X2))) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,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)],[d11,d3]) ).
cnf(d13,plain,
~ 'is$ua$utheorem'(implies(implies(implies(y,u),y),y)),
inference(resolution,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
( 'is$ua$utheorem'(implies(implies(X2,X0),X0))
| ~ 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d15,plain,
( 'is$ua$utheorem'(implies(implies(X2,X0),X0))
| ~ 'is$ua$utheorem'(implies(implies(not(not(X0)),X1),X2)) ),
inference(resolution,[status(thm)],[d14,c3]) ).
cnf(d16,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)],[d6,d0]) ).
cnf(d17,plain,
( 'is$ua$utheorem'(implies(implies(X1,X2),implies(X0,X2)))
| ~ 'is$ua$utheorem'(implies(X0,implies(not(X1),X1))) ),
inference(resolution,[status(thm)],[d16,c2]) ).
cnf(d18,plain,
( ~ 'is$ua$utheorem'(implies(X1,not(X0)))
| 'is$ua$utheorem'(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d19,plain,
( 'is$ua$utheorem'(implies(X1,X3))
| ~ 'is$ua$utheorem'(implies(implies(X0,X2),X3))
| ~ 'is$ua$utheorem'(implies(X0,not(X1))) ),
inference(resolution,[status(thm)],[d18,d2]) ).
cnf(d20,plain,
( ~ 'is$ua$utheorem'(implies(not(X1),X2))
| ~ 'is$ua$utheorem'(implies(X2,not(X0)))
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d19,d7]) ).
cnf(d21,plain,
( 'is$ua$utheorem'(implies(X2,X0))
| ~ 'is$ua$utheorem'(implies(implies(not(not(X0)),X1),not(X2))) ),
inference(resolution,[status(thm)],[d20,c3]) ).
cnf(d22,plain,
( ~ 'is$ua$utheorem'(implies(not(not(X0)),not(not(X1))))
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d21,d7]) ).
cnf(d23,plain,
'is$ua$utheorem'(implies(X0,X0)),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d24,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),
inference(resolution,[status(thm)],[d17,d23]) ).
cnf(d25,plain,
( 'is$ua$utheorem'(implies(X2,X1))
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d9,d2]) ).
cnf(d26,plain,
'is$ua$utheorem'(implies(X0,implies(not(implies(not(X0),X1)),X2))),
inference(resolution,[status(thm)],[d5,c3]) ).
cnf(d27,plain,
'is$ua$utheorem'(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),
inference(resolution,[status(thm)],[d17,d26]) ).
cnf(d28,plain,
( 'is$ua$utheorem'(implies(X3,implies(X0,X2)))
| ~ 'is$ua$utheorem'(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[d27,d25]) ).
cnf(d29,plain,
'is$ua$utheorem'(implies(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[d28,c2]) ).
cnf(d30,plain,
( 'is$ua$utheorem'(implies(X2,X1))
| ~ 'is$ua$utheorem'(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[d29,d2]) ).
cnf(d31,plain,
'is$ua$utheorem'(implies(X0,implies(implies(not(X1),X1),X1))),
inference(resolution,[status(thm)],[d30,d24]) ).
cnf(d32,plain,
( ~ 'is$ua$utheorem'(implies(X2,implies(X1,X3)))
| 'is$ua$utheorem'(implies(implies(X0,X1),implies(X2,implies(X0,X3)))) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d33,plain,
( ~ 'is$ua$utheorem'(implies(X3,X1))
| 'is$ua$utheorem'(implies(X0,implies(X3,X2)))
| ~ 'is$ua$utheorem'(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[d32,c0]) ).
cnf(d34,plain,
'is$ua$utheorem'(implies(X0,implies(implies(X1,X2),implies(not(X0),X2)))),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d35,plain,
( 'is$ua$utheorem'(implies(X2,X3))
| ~ 'is$ua$utheorem'(implies(implies(implies(X0,X1),implies(not(X2),X1)),X3)) ),
inference(resolution,[status(thm)],[d34,d2]) ).
cnf(d36,plain,
'is$ua$utheorem'(implies(implies(X0,implies(not(X1),X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[d31,d10]) ).
cnf(d37,plain,
'is$ua$utheorem'(implies(X0,implies(implies(X1,X0),X0))),
inference(resolution,[status(thm)],[d36,d35]) ).
cnf(d38,plain,
( 'is$ua$utheorem'(implies(X2,implies(X0,X2)))
| ~ 'is$ua$utheorem'(implies(X0,implies(X1,X2))) ),
inference(resolution,[status(thm)],[d37,d33]) ).
cnf(d39,plain,
'is$ua$utheorem'(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[d38,d31]) ).
cnf(d40,plain,
( 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d39,d2]) ).
cnf(d41,plain,
( 'is$ua$utheorem'(implies(X0,X3))
| ~ 'is$ua$utheorem'(implies(implies(not(implies(not(X0),X1)),X2),X3)) ),
inference(resolution,[status(thm)],[d26,d2]) ).
cnf(d42,plain,
( 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(implies(not(X0),not(implies(not(X1),X2)))) ),
inference(resolution,[status(thm)],[d7,d41]) ).
cnf(d43,plain,
( ~ 'is$ua$utheorem'(implies(X0,implies(not(X1),X1)))
| 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d36,c0]) ).
cnf(d44,plain,
'is$ua$utheorem'(implies(implies(X0,not(not(implies(X0,X1)))),implies(X0,X1))),
inference(resolution,[status(thm)],[d10,c3]) ).
cnf(d45,plain,
'is$ua$utheorem'(implies(not(not(implies(X0,X1))),implies(X0,X1))),
inference(resolution,[status(thm)],[d40,d44]) ).
cnf(d46,plain,
'is$ua$utheorem'(implies(not(not(implies(not(X0),X0))),X0)),
inference(resolution,[status(thm)],[d45,d43]) ).
cnf(d47,plain,
'is$ua$utheorem'(implies(X0,not(implies(not(not(X0)),not(X0))))),
inference(resolution,[status(thm)],[d46,d8]) ).
cnf(d48,plain,
'is$ua$utheorem'(implies(not(not(X0)),X0)),
inference(resolution,[status(thm)],[d47,d42]) ).
cnf(d49,plain,
'is$ua$utheorem'(implies(X0,not(not(X0)))),
inference(resolution,[status(thm)],[d48,d8]) ).
cnf(d50,plain,
'is$ua$utheorem'(implies(X0,not(not(implies(X1,X0))))),
inference(resolution,[status(thm)],[d49,d40]) ).
cnf(d51,plain,
'is$ua$utheorem'(implies(X0,implies(X1,not(not(X0))))),
inference(resolution,[status(thm)],[d50,d22]) ).
cnf(d52,plain,
'is$ua$utheorem'(implies(implies(not(not(X0)),X1),implies(X0,X1))),
inference(resolution,[status(thm)],[d51,d17]) ).
cnf(d53,plain,
'is$ua$utheorem'(implies(implies(implies(X0,X1),X0),X0)),
inference(resolution,[status(thm)],[d52,d15]) ).
cnf(d54,plain,
$false,
inference(resolution,[status(thm)],[d53,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL372+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n020.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Fri Sep 25 22:21:54 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 109.68/27.44 % SZS status Theorem for theBenchmark.p
% 109.68/27.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------