%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG223+2 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 06:48:09 AM UTC 2026
% Result : Theorem 147.41s 23.51s
% Output : CNFRefutation 147.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 47 ( 10 unt; 0 def)
% Number of atoms : 152 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 195 ( 90 ~; 85 |; 5 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_closure3,axiom,
! [X0,X1] :
( 'm1$upboole'(X1,X0)
=> ! [X2] :
( 'm1$usubset$u1'(X2,'k1$uzfmisc$u1'('k1$uclosure2'(X0,X1)))
=> ! [X3] :
( 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('k1$uclosure2'(X0,X1)))
=> ( 'r1$uclosure3'(X0,X1,X2,X3)
<=> ! [X4] :
~ ( ! [X5] :
~ ( 'r1$utarski'(X4,X5)
& 'r2$uhidden'(X5,X2) )
& 'r2$uhidden'(X4,X3) ) ) ) ) ) ).
fof(t1_xboole_1,axiom,
! [X0,X1,X2] :
( ( 'r1$utarski'(X1,X2)
& 'r1$utarski'(X0,X1) )
=> 'r1$utarski'(X0,X2) ) ).
fof(t4_closure3,conjecture,
! [X0,X1] :
( 'm1$upboole'(X1,X0)
=> ! [X2] :
( 'm1$usubset$u1'(X2,'k1$uzfmisc$u1'('k1$uclosure2'(X0,X1)))
=> ! [X3] :
( 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('k1$uclosure2'(X0,X1)))
=> ! [X4] :
( 'm1$usubset$u1'(X4,'k1$uzfmisc$u1'('k1$uclosure2'(X0,X1)))
=> ( ( 'r1$uclosure3'(X0,X1,X4,X3)
& 'r1$uclosure3'(X0,X1,X3,X2) )
=> 'r1$uclosure3'(X0,X1,X4,X2) ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( 'm1$upboole'(X1,X0)
=> ! [X2] :
( 'm1$usubset$u1'(X2,'k1$uzfmisc$u1'('k1$uclosure2'(X0,X1)))
=> ! [X3] :
( 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('k1$uclosure2'(X0,X1)))
=> ! [X4] :
( 'm1$usubset$u1'(X4,'k1$uzfmisc$u1'('k1$uclosure2'(X0,X1)))
=> ( ( 'r1$uclosure3'(X0,X1,X4,X3)
& 'r1$uclosure3'(X0,X1,X3,X2) )
=> 'r1$uclosure3'(X0,X1,X4,X2) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t4_closure3]) ).
cnf(c1,plain,
( ~ 'r2$uhidden'(X4,X0)
| ~ 'r1$uclosure3'(X1,X2,X3,X0)
| ~ 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2)))
| ~ 'm1$upboole'(X2,X1)
| 'r2$uhidden'(sK9(X3,X4),X3)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2))) ),
inference(clausification,[status(esa)],[d1_closure3]) ).
cnf(c2,plain,
( ~ 'r2$uhidden'(X3,X0)
| ~ 'r1$uclosure3'(X1,X2,X4,X0)
| ~ 'm1$usubset$u1'(X4,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2)))
| ~ 'm1$upboole'(X2,X1)
| 'r1$utarski'(X3,sK9(X4,X3))
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2))) ),
inference(clausification,[status(esa)],[d1_closure3]) ).
cnf(c3,plain,
( ~ 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2)))
| 'r2$uhidden'(sK10(X3,X0),X0)
| ~ 'm1$upboole'(X2,X1)
| 'r1$uclosure3'(X1,X2,X3,X0)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2))) ),
inference(clausification,[status(esa)],[d1_closure3]) ).
cnf(c4,plain,
( ~ 'r1$utarski'(sK10(X3,X0),X4)
| ~ 'r2$uhidden'(X4,X3)
| ~ 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2)))
| ~ 'm1$upboole'(X2,X1)
| 'r1$uclosure3'(X1,X2,X3,X0)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2))) ),
inference(clausification,[status(esa)],[d1_closure3]) ).
cnf(c61,plain,
( 'r1$utarski'(X0,X2)
| ~ 'r1$utarski'(X1,X2)
| ~ 'r1$utarski'(X0,X1) ),
inference(clausification,[status(esa)],[t1_xboole_1]) ).
cnf(c517,plain,
'm1$upboole'(sK803,sK802),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c518,plain,
'm1$usubset$u1'(sK804,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c519,plain,
'm1$usubset$u1'(sK805,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c520,plain,
'm1$usubset$u1'(sK806,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c521,plain,
'r1$uclosure3'(sK802,sK803,sK805,sK804),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c522,plain,
'r1$uclosure3'(sK802,sK803,sK806,sK805),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c523,plain,
~ 'r1$uclosure3'(sK802,sK803,sK806,sK804),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'r2$uhidden'(sK9(X0,X1),X0)
| ~ 'r2$uhidden'(X1,sK804)
| ~ 'r1$uclosure3'(sK802,sK803,X0,sK804)
| ~ 'm1$upboole'(sK803,sK802)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))) ),
inference(resolution,[status(thm)],[c1,c518]) ).
cnf(d1,plain,
( 'r2$uhidden'(sK9(X0,X1),X0)
| ~ 'r2$uhidden'(X1,sK804)
| ~ 'r1$uclosure3'(sK802,sK803,X0,sK804)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))) ),
inference(resolution,[status(thm)],[c517,d0]) ).
cnf(d2,plain,
( 'r2$uhidden'(sK9(sK805,X0),sK805)
| ~ 'r2$uhidden'(X0,sK804)
| ~ 'r1$uclosure3'(sK802,sK803,sK805,sK804) ),
inference(resolution,[status(thm)],[d1,c519]) ).
cnf(d3,plain,
( 'r2$uhidden'(sK9(sK805,X0),sK805)
| ~ 'r2$uhidden'(X0,sK804) ),
inference(resolution,[status(thm)],[c521,d2]) ).
cnf(d4,plain,
( 'r2$uhidden'(sK9(X0,X1),X0)
| ~ 'r2$uhidden'(X1,sK805)
| ~ 'r1$uclosure3'(sK802,sK803,X0,sK805)
| ~ 'm1$upboole'(sK803,sK802)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))) ),
inference(resolution,[status(thm)],[c1,c519]) ).
cnf(d5,plain,
( 'r2$uhidden'(sK9(X0,X1),X0)
| ~ 'r2$uhidden'(X1,sK805)
| ~ 'r1$uclosure3'(sK802,sK803,X0,sK805)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))) ),
inference(resolution,[status(thm)],[c517,d4]) ).
cnf(d6,plain,
( 'r2$uhidden'(sK9(sK806,X0),sK806)
| ~ 'r2$uhidden'(X0,sK805)
| ~ 'r1$uclosure3'(sK802,sK803,sK806,sK805) ),
inference(resolution,[status(thm)],[d5,c520]) ).
cnf(d7,plain,
( 'r2$uhidden'(sK9(sK806,X0),sK806)
| ~ 'r2$uhidden'(X0,sK805) ),
inference(resolution,[status(thm)],[c522,d6]) ).
cnf(d8,plain,
( ~ 'r1$utarski'(sK10(X0,sK804),X1)
| ~ 'r2$uhidden'(X1,X0)
| 'r1$uclosure3'(sK802,sK803,X0,sK804)
| ~ 'm1$upboole'(sK803,sK802)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))) ),
inference(resolution,[status(thm)],[c4,c518]) ).
cnf(d9,plain,
( ~ 'r1$utarski'(sK10(X0,sK804),X1)
| ~ 'r2$uhidden'(X1,X0)
| 'r1$uclosure3'(sK802,sK803,X0,sK804)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))) ),
inference(resolution,[status(thm)],[c517,d8]) ).
cnf(d10,plain,
( ~ 'r1$utarski'(sK10(sK806,sK804),X0)
| ~ 'r2$uhidden'(X0,sK806)
| 'r1$uclosure3'(sK802,sK803,sK806,sK804) ),
inference(resolution,[status(thm)],[d9,c520]) ).
cnf(d11,plain,
( ~ 'r1$utarski'(sK10(sK806,sK804),X0)
| ~ 'r2$uhidden'(X0,sK806) ),
inference(resolution,[status(thm)],[c523,d10]) ).
cnf(d12,plain,
( 'r1$utarski'(X1,sK9(X0,X1))
| ~ 'r2$uhidden'(X1,sK805)
| ~ 'r1$uclosure3'(sK802,sK803,X0,sK805)
| ~ 'm1$upboole'(sK803,sK802)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))) ),
inference(resolution,[status(thm)],[c2,c519]) ).
cnf(d13,plain,
( 'r1$utarski'(X1,sK9(X0,X1))
| ~ 'r2$uhidden'(X1,sK805)
| ~ 'r1$uclosure3'(sK802,sK803,X0,sK805)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))) ),
inference(resolution,[status(thm)],[c517,d12]) ).
cnf(d14,plain,
( 'r1$utarski'(X0,sK9(sK806,X0))
| ~ 'r2$uhidden'(X0,sK805)
| ~ 'r1$uclosure3'(sK802,sK803,sK806,sK805) ),
inference(resolution,[status(thm)],[d13,c520]) ).
cnf(d15,plain,
( 'r1$utarski'(X0,sK9(sK806,X0))
| ~ 'r2$uhidden'(X0,sK805) ),
inference(resolution,[status(thm)],[c522,d14]) ).
cnf(d16,plain,
( 'r1$utarski'(X1,sK9(X0,X1))
| ~ 'r2$uhidden'(X1,sK804)
| ~ 'r1$uclosure3'(sK802,sK803,X0,sK804)
| ~ 'm1$upboole'(sK803,sK802)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))) ),
inference(resolution,[status(thm)],[c2,c518]) ).
cnf(d17,plain,
( 'r1$utarski'(X1,sK9(X0,X1))
| ~ 'r2$uhidden'(X1,sK804)
| ~ 'r1$uclosure3'(sK802,sK803,X0,sK804)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))) ),
inference(resolution,[status(thm)],[c517,d16]) ).
cnf(d18,plain,
( 'r1$utarski'(X0,sK9(sK805,X0))
| ~ 'r2$uhidden'(X0,sK804)
| ~ 'r1$uclosure3'(sK802,sK803,sK805,sK804) ),
inference(resolution,[status(thm)],[d17,c519]) ).
cnf(d19,plain,
( 'r1$utarski'(X0,sK9(sK805,X0))
| ~ 'r2$uhidden'(X0,sK804) ),
inference(resolution,[status(thm)],[c521,d18]) ).
cnf(d20,plain,
( ~ 'r2$uhidden'(X0,sK804)
| 'r1$utarski'(X0,X1)
| ~ 'r1$utarski'(sK9(sK805,X0),X1) ),
inference(resolution,[status(thm)],[c61,d19]) ).
cnf(d21,plain,
( ~ 'r2$uhidden'(sK9(sK805,X0),sK805)
| 'r1$utarski'(X0,sK9(sK806,sK9(sK805,X0)))
| ~ 'r2$uhidden'(X0,sK804) ),
inference(resolution,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
( ~ 'r2$uhidden'(sK9(sK806,sK9(sK805,sK10(sK806,sK804))),sK806)
| ~ 'r2$uhidden'(sK9(sK805,sK10(sK806,sK804)),sK805)
| ~ 'r2$uhidden'(sK10(sK806,sK804),sK804) ),
inference(resolution,[status(thm)],[d21,d11]) ).
cnf(d23,plain,
( 'r2$uhidden'(sK10(X0,sK804),sK804)
| 'r1$uclosure3'(sK802,sK803,X0,sK804)
| ~ 'm1$upboole'(sK803,sK802)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))) ),
inference(resolution,[status(thm)],[c3,c518]) ).
cnf(d24,plain,
( 'r2$uhidden'(sK10(X0,sK804),sK804)
| 'r1$uclosure3'(sK802,sK803,X0,sK804)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK802,sK803))) ),
inference(resolution,[status(thm)],[c517,d23]) ).
cnf(d25,plain,
( 'r2$uhidden'(sK10(sK806,sK804),sK804)
| 'r1$uclosure3'(sK802,sK803,sK806,sK804) ),
inference(resolution,[status(thm)],[d24,c520]) ).
cnf(d26,plain,
'r2$uhidden'(sK10(sK806,sK804),sK804),
inference(resolution,[status(thm)],[c523,d25]) ).
cnf(d27,plain,
( ~ 'r2$uhidden'(sK9(sK806,sK9(sK805,sK10(sK806,sK804))),sK806)
| ~ 'r2$uhidden'(sK9(sK805,sK10(sK806,sK804)),sK805) ),
inference(resolution,[status(thm)],[d26,d22]) ).
cnf(d28,plain,
( ~ 'r2$uhidden'(sK9(sK805,sK10(sK806,sK804)),sK805)
| ~ 'r2$uhidden'(sK9(sK805,sK10(sK806,sK804)),sK805) ),
inference(resolution,[status(thm)],[d27,d7]) ).
cnf(d29,plain,
~ 'r2$uhidden'(sK10(sK806,sK804),sK804),
inference(resolution,[status(thm)],[d28,d3]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[d26,d29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG223+2 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sat Sep 26 21:36:06 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 147.41/23.51 % SZS status Theorem for theBenchmark.p
% 147.41/23.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------