%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG224+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 25.10s 4.10s
% Output : CNFRefutation 25.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 51 ( 13 unt; 0 def)
% Number of atoms : 161 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 207 ( 97 ~; 90 |; 5 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 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 : 83 ( 1 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d2_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$uclosure2'(X0,X1)))
=> ( 'r2$uclosure3'(X0,X1,X2,X3)
<=> ! [X4] :
~ ( ! [X5] :
~ ( 'r1$utarski'(X5,X4)
& 'r2$uhidden'(X5,X3) )
& 'r2$uhidden'(X4,X2) ) ) ) ) ) ).
fof(reflexivity_r1_tarski,axiom,
! [X0,X1] : 'r1$utarski'(X0,X0) ).
fof(t1_xboole_1,axiom,
! [X0,X1,X2] :
( ( 'r1$utarski'(X1,X2)
& 'r1$utarski'(X0,X1) )
=> 'r1$utarski'(X0,X2) ) ).
fof(t5_closure3,conjecture,
! [X0,X1] :
( 'm1$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$uclosure2'(X0,X1)))
=> ( ( 'r2$uclosure3'(X0,X1,X3,X4)
& 'r2$uclosure3'(X0,X1,X2,X3) )
=> 'r2$uclosure3'(X0,X1,X2,X4) ) ) ) ) ) ).
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)))
=> ( ( 'r2$uclosure3'(X0,X1,X3,X4)
& 'r2$uclosure3'(X0,X1,X2,X3) )
=> 'r2$uclosure3'(X0,X1,X2,X4) ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t5_closure3]) ).
cnf(c8,plain,
( ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(X3,X2)))
| ~ 'm1$usubset$u1'(X4,'k1$uzfmisc$u1'('k1$uclosure2'(X3,X2)))
| ~ 'r2$uclosure3'(X3,X2,X4,X0)
| ~ 'r2$uhidden'(X1,X4)
| ~ 'm1$upboole'(X2,X3)
| 'r2$uhidden'(sK13(X0,X1),X0) ),
inference(clausification,[status(esa)],[d2_closure3]) ).
cnf(c9,plain,
( ~ 'm1$usubset$u1'(X4,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X0)))
| ~ 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X0)))
| ~ 'r2$uclosure3'(X1,X0,X3,X4)
| 'r1$utarski'(sK13(X4,X2),X2)
| ~ 'r2$uhidden'(X2,X3)
| ~ 'm1$upboole'(X0,X1) ),
inference(clausification,[status(esa)],[d2_closure3]) ).
cnf(c10,plain,
( ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('k1$uclosure2'(X3,X2)))
| 'r2$uclosure3'(X3,X2,X0,X1)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(X3,X2)))
| ~ 'm1$upboole'(X2,X3)
| 'r2$uhidden'(sK14(X0,X1),X0) ),
inference(clausification,[status(esa)],[d2_closure3]) ).
cnf(c11,plain,
( ~ 'r2$uhidden'(X4,X3)
| ~ 'r1$utarski'(X4,sK14(X2,X3))
| ~ 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X0)))
| 'r2$uclosure3'(X1,X0,X2,X3)
| ~ 'm1$usubset$u1'(X2,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X0)))
| ~ 'm1$upboole'(X0,X1) ),
inference(clausification,[status(esa)],[d2_closure3]) ).
cnf(c61,plain,
'r1$utarski'(X0,X0),
inference(clausification,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(c64,plain,
( 'r1$utarski'(X0,X2)
| ~ 'r1$utarski'(X1,X2)
| ~ 'r1$utarski'(X0,X1) ),
inference(clausification,[status(esa)],[t1_xboole_1]) ).
cnf(c73,plain,
'm1$upboole'(sK74,sK73),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c74,plain,
'm1$usubset$u1'(sK75,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c75,plain,
'm1$usubset$u1'(sK76,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c76,plain,
'm1$usubset$u1'(sK77,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c77,plain,
'r2$uclosure3'(sK73,sK74,sK75,sK76),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c78,plain,
'r2$uclosure3'(sK73,sK74,sK76,sK77),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c79,plain,
~ 'r2$uclosure3'(sK73,sK74,sK75,sK77),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'r2$uclosure3'(sK73,sK74,sK75,X1)
| ~ 'm1$upboole'(sK74,sK73)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74)))
| 'r2$uhidden'(sK13(X1,X0),X1)
| ~ 'r2$uhidden'(X0,sK75) ),
inference(resolution,[status(thm)],[c8,c74]) ).
cnf(d1,plain,
( ~ 'r2$uclosure3'(sK73,sK74,sK75,X1)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74)))
| 'r2$uhidden'(sK13(X1,X0),X1)
| ~ 'r2$uhidden'(X0,sK75) ),
inference(resolution,[status(thm)],[c73,d0]) ).
cnf(d2,plain,
( ~ 'r2$uclosure3'(sK73,sK74,sK75,sK76)
| 'r2$uhidden'(sK13(sK76,X0),sK76)
| ~ 'r2$uhidden'(X0,sK75) ),
inference(resolution,[status(thm)],[d1,c75]) ).
cnf(d3,plain,
( 'r2$uhidden'(sK13(sK76,X0),sK76)
| ~ 'r2$uhidden'(X0,sK75) ),
inference(resolution,[status(thm)],[c77,d2]) ).
cnf(d4,plain,
( ~ 'r2$uclosure3'(sK73,sK74,sK76,X1)
| ~ 'm1$upboole'(sK74,sK73)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74)))
| 'r2$uhidden'(sK13(X1,X0),X1)
| ~ 'r2$uhidden'(X0,sK76) ),
inference(resolution,[status(thm)],[c8,c75]) ).
cnf(d5,plain,
( ~ 'r2$uclosure3'(sK73,sK74,sK76,X1)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74)))
| 'r2$uhidden'(sK13(X1,X0),X1)
| ~ 'r2$uhidden'(X0,sK76) ),
inference(resolution,[status(thm)],[c73,d4]) ).
cnf(d6,plain,
( ~ 'r2$uclosure3'(sK73,sK74,sK76,sK77)
| 'r2$uhidden'(sK13(sK77,X0),sK77)
| ~ 'r2$uhidden'(X0,sK76) ),
inference(resolution,[status(thm)],[d5,c76]) ).
cnf(d7,plain,
( 'r2$uhidden'(sK13(sK77,X0),sK77)
| ~ 'r2$uhidden'(X0,sK76) ),
inference(resolution,[status(thm)],[c78,d6]) ).
cnf(d8,plain,
( 'r1$utarski'(sK13(X1,X0),X0)
| ~ 'r2$uclosure3'(sK73,sK74,sK75,X1)
| ~ 'm1$upboole'(sK74,sK73)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74)))
| ~ 'r2$uhidden'(X0,sK75) ),
inference(resolution,[status(thm)],[c9,c74]) ).
cnf(d9,plain,
( 'r1$utarski'(sK13(X1,X0),X0)
| ~ 'r2$uclosure3'(sK73,sK74,sK75,X1)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74)))
| ~ 'r2$uhidden'(X0,sK75) ),
inference(resolution,[status(thm)],[c73,d8]) ).
cnf(d10,plain,
( 'r1$utarski'(sK13(sK76,X0),X0)
| ~ 'r2$uclosure3'(sK73,sK74,sK75,sK76)
| ~ 'r2$uhidden'(X0,sK75) ),
inference(resolution,[status(thm)],[d9,c75]) ).
cnf(d11,plain,
( 'r1$utarski'(sK13(sK76,X0),X0)
| ~ 'r2$uhidden'(X0,sK75) ),
inference(resolution,[status(thm)],[c77,d10]) ).
cnf(d12,plain,
( ~ 'r2$uhidden'(X0,sK75)
| 'r1$utarski'(sK13(sK76,X0),X1)
| ~ 'r1$utarski'(X0,X1) ),
inference(resolution,[status(thm)],[c64,d11]) ).
cnf(d13,plain,
( ~ 'r1$utarski'(X0,sK14(sK75,X1))
| 'r2$uclosure3'(sK73,sK74,sK75,X1)
| ~ 'm1$upboole'(sK74,sK73)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74)))
| ~ 'r2$uhidden'(X0,X1) ),
inference(resolution,[status(thm)],[c11,c74]) ).
cnf(d14,plain,
( ~ 'r1$utarski'(X0,sK14(sK75,X1))
| 'r2$uclosure3'(sK73,sK74,sK75,X1)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74)))
| ~ 'r2$uhidden'(X0,X1) ),
inference(resolution,[status(thm)],[c73,d13]) ).
cnf(d15,plain,
( ~ 'r1$utarski'(X0,sK14(sK75,sK77))
| 'r2$uclosure3'(sK73,sK74,sK75,sK77)
| ~ 'r2$uhidden'(X0,sK77) ),
inference(resolution,[status(thm)],[d14,c76]) ).
cnf(d16,plain,
( ~ 'r1$utarski'(X0,sK14(sK75,sK77))
| ~ 'r2$uhidden'(X0,sK77) ),
inference(resolution,[status(thm)],[c79,d15]) ).
cnf(d17,plain,
( 'r1$utarski'(sK13(X1,X0),X0)
| ~ 'r2$uclosure3'(sK73,sK74,sK76,X1)
| ~ 'm1$upboole'(sK74,sK73)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74)))
| ~ 'r2$uhidden'(X0,sK76) ),
inference(resolution,[status(thm)],[c9,c75]) ).
cnf(d18,plain,
( 'r1$utarski'(sK13(X1,X0),X0)
| ~ 'r2$uclosure3'(sK73,sK74,sK76,X1)
| ~ 'm1$usubset$u1'(X1,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74)))
| ~ 'r2$uhidden'(X0,sK76) ),
inference(resolution,[status(thm)],[c73,d17]) ).
cnf(d19,plain,
( 'r1$utarski'(sK13(sK77,X0),X0)
| ~ 'r2$uclosure3'(sK73,sK74,sK76,sK77)
| ~ 'r2$uhidden'(X0,sK76) ),
inference(resolution,[status(thm)],[d18,c76]) ).
cnf(d20,plain,
( 'r1$utarski'(sK13(sK77,X0),X0)
| ~ 'r2$uhidden'(X0,sK76) ),
inference(resolution,[status(thm)],[c78,d19]) ).
cnf(d21,plain,
( ~ 'r2$uhidden'(X0,sK76)
| 'r1$utarski'(sK13(sK77,X0),X1)
| ~ 'r1$utarski'(X0,X1) ),
inference(resolution,[status(thm)],[c64,d20]) ).
cnf(d22,plain,
( ~ 'r2$uhidden'(sK13(sK77,X0),sK77)
| ~ 'r1$utarski'(X0,sK14(sK75,sK77))
| ~ 'r2$uhidden'(X0,sK76) ),
inference(resolution,[status(thm)],[d21,d16]) ).
cnf(d23,plain,
( ~ 'r1$utarski'(X0,sK14(sK75,sK77))
| ~ 'r2$uhidden'(X0,sK75)
| ~ 'r2$uhidden'(sK13(sK77,sK13(sK76,X0)),sK77)
| ~ 'r2$uhidden'(sK13(sK76,X0),sK76) ),
inference(resolution,[status(thm)],[d22,d12]) ).
cnf(d24,plain,
( ~ 'r2$uhidden'(sK13(sK76,X0),sK76)
| ~ 'r1$utarski'(X0,sK14(sK75,sK77))
| ~ 'r2$uhidden'(sK13(sK76,X0),sK76)
| ~ 'r2$uhidden'(X0,sK75) ),
inference(resolution,[status(thm)],[d23,d7]) ).
cnf(d25,plain,
( ~ 'r2$uhidden'(sK13(sK76,sK14(sK75,sK77)),sK76)
| ~ 'r2$uhidden'(sK14(sK75,sK77),sK75) ),
inference(resolution,[status(thm)],[d24,c61]) ).
cnf(d26,plain,
( 'r2$uclosure3'(sK73,sK74,sK75,X0)
| ~ 'm1$upboole'(sK74,sK73)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74)))
| 'r2$uhidden'(sK14(sK75,X0),sK75) ),
inference(resolution,[status(thm)],[c10,c74]) ).
cnf(d27,plain,
( 'r2$uclosure3'(sK73,sK74,sK75,X0)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK73,sK74)))
| 'r2$uhidden'(sK14(sK75,X0),sK75) ),
inference(resolution,[status(thm)],[c73,d26]) ).
cnf(d28,plain,
( 'r2$uclosure3'(sK73,sK74,sK75,sK77)
| 'r2$uhidden'(sK14(sK75,sK77),sK75) ),
inference(resolution,[status(thm)],[d27,c76]) ).
cnf(d29,plain,
'r2$uhidden'(sK14(sK75,sK77),sK75),
inference(resolution,[status(thm)],[c79,d28]) ).
cnf(d30,plain,
~ 'r2$uhidden'(sK13(sK76,sK14(sK75,sK77)),sK76),
inference(resolution,[status(thm)],[d29,d25]) ).
cnf(d31,plain,
~ 'r2$uhidden'(sK14(sK75,sK77),sK75),
inference(resolution,[status(thm)],[d30,d3]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[d29,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG224+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 21:36:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.10/4.10 % SZS status Theorem for theBenchmark.p
% 25.10/4.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------