%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG224+3 : 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 38.64s 18.65s
% Output : CNFRefutation 38.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 52 ( 10 unt; 0 def)
% Number of atoms : 167 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 211 ( 96 ~; 95 |; 4 &)
% ( 2 <=>; 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn 19 !; 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$uhidden'(X4,X2) ) ) ) ) ) ).
fof(d3_tarski,axiom,
! [X0,X1] :
( 'r1$utarski'(X0,X1)
<=> ! [X2] :
( 'r2$uhidden'(X2,X0)
=> 'r2$uhidden'(X2,X1) ) ) ).
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(c1,plain,
( ~ 'r2$uclosure3'(X1,X2,X3,X0)
| 'r2$uhidden'(sK9(X0,X4),X0)
| ~ 'r2$uhidden'(X4,X3)
| ~ 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2)))
| ~ 'm1$upboole'(X2,X1)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2))) ),
inference(clausification,[status(esa)],[d2_closure3]) ).
cnf(c2,plain,
( ~ 'r2$uclosure3'(X1,X2,X4,X0)
| ~ 'r2$uhidden'(X3,X4)
| ~ 'm1$usubset$u1'(X4,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2)))
| ~ 'm1$upboole'(X2,X1)
| 'r1$utarski'(sK9(X0,X3),X3)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2))) ),
inference(clausification,[status(esa)],[d2_closure3]) ).
cnf(c3,plain,
( 'r2$uhidden'(sK10(X3,X0),X3)
| 'r2$uclosure3'(X1,X2,X3,X0)
| ~ 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2)))
| ~ 'm1$upboole'(X2,X1)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2))) ),
inference(clausification,[status(esa)],[d2_closure3]) ).
cnf(c4,plain,
( ~ 'r1$utarski'(X4,sK10(X3,X0))
| ~ 'm1$usubset$u1'(X3,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2)))
| ~ 'r2$uhidden'(X4,X0)
| ~ 'm1$upboole'(X2,X1)
| 'r2$uclosure3'(X1,X2,X3,X0)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(X1,X2))) ),
inference(clausification,[status(esa)],[d2_closure3]) ).
cnf(c27,plain,
( 'r2$uhidden'(X2,X1)
| ~ 'r2$uhidden'(X2,X0)
| ~ 'r1$utarski'(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c28,plain,
( 'r2$uhidden'(sK30(X0,X1),X0)
| 'r1$utarski'(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c29,plain,
( ~ 'r2$uhidden'(sK30(X0,X1),X1)
| 'r1$utarski'(X0,X1) ),
inference(clausification,[status(esa)],[d3_tarski]) ).
cnf(c805,plain,
'm1$upboole'(sK1157,sK1156),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c806,plain,
'm1$usubset$u1'(sK1158,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c807,plain,
'm1$usubset$u1'(sK1159,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c808,plain,
'm1$usubset$u1'(sK1160,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c809,plain,
'r2$uclosure3'(sK1156,sK1157,sK1158,sK1159),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c810,plain,
'r2$uclosure3'(sK1156,sK1157,sK1159,sK1160),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c811,plain,
~ 'r2$uclosure3'(sK1156,sK1157,sK1158,sK1160),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'r2$uhidden'(sK9(X0,X1),X0)
| ~ 'r2$uhidden'(X1,sK1158)
| ~ 'r2$uclosure3'(sK1156,sK1157,sK1158,X0)
| ~ 'm1$upboole'(sK1157,sK1156)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))) ),
inference(resolution,[status(thm)],[c1,c806]) ).
cnf(d1,plain,
( 'r2$uhidden'(sK9(X0,X1),X0)
| ~ 'r2$uhidden'(X1,sK1158)
| ~ 'r2$uclosure3'(sK1156,sK1157,sK1158,X0)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))) ),
inference(resolution,[status(thm)],[c805,d0]) ).
cnf(d2,plain,
( 'r2$uhidden'(sK9(sK1159,X0),sK1159)
| ~ 'r2$uhidden'(X0,sK1158)
| ~ 'r2$uclosure3'(sK1156,sK1157,sK1158,sK1159) ),
inference(resolution,[status(thm)],[d1,c807]) ).
cnf(d3,plain,
( 'r2$uhidden'(sK9(sK1159,X0),sK1159)
| ~ 'r2$uhidden'(X0,sK1158) ),
inference(resolution,[status(thm)],[c809,d2]) ).
cnf(d4,plain,
( 'r2$uhidden'(sK9(X0,X1),X0)
| ~ 'r2$uhidden'(X1,sK1159)
| ~ 'r2$uclosure3'(sK1156,sK1157,sK1159,X0)
| ~ 'm1$upboole'(sK1157,sK1156)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))) ),
inference(resolution,[status(thm)],[c1,c807]) ).
cnf(d5,plain,
( 'r2$uhidden'(sK9(X0,X1),X0)
| ~ 'r2$uhidden'(X1,sK1159)
| ~ 'r2$uclosure3'(sK1156,sK1157,sK1159,X0)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))) ),
inference(resolution,[status(thm)],[c805,d4]) ).
cnf(d6,plain,
( 'r2$uhidden'(sK9(sK1160,X0),sK1160)
| ~ 'r2$uhidden'(X0,sK1159)
| ~ 'r2$uclosure3'(sK1156,sK1157,sK1159,sK1160) ),
inference(resolution,[status(thm)],[d5,c808]) ).
cnf(d7,plain,
( 'r2$uhidden'(sK9(sK1160,X0),sK1160)
| ~ 'r2$uhidden'(X0,sK1159) ),
inference(resolution,[status(thm)],[c810,d6]) ).
cnf(d8,plain,
( ~ 'r1$utarski'(X1,sK10(X0,sK1160))
| ~ 'r2$uhidden'(X1,sK1160)
| 'r2$uclosure3'(sK1156,sK1157,X0,sK1160)
| ~ 'm1$upboole'(sK1157,sK1156)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))) ),
inference(resolution,[status(thm)],[c4,c808]) ).
cnf(d9,plain,
( ~ 'r1$utarski'(X1,sK10(X0,sK1160))
| ~ 'r2$uhidden'(X1,sK1160)
| 'r2$uclosure3'(sK1156,sK1157,X0,sK1160)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))) ),
inference(resolution,[status(thm)],[c805,d8]) ).
cnf(d10,plain,
( ~ 'r1$utarski'(X0,sK10(sK1158,sK1160))
| ~ 'r2$uhidden'(X0,sK1160)
| 'r2$uclosure3'(sK1156,sK1157,sK1158,sK1160) ),
inference(resolution,[status(thm)],[d9,c806]) ).
cnf(d11,plain,
( ~ 'r1$utarski'(X0,sK10(sK1158,sK1160))
| ~ 'r2$uhidden'(X0,sK1160) ),
inference(resolution,[status(thm)],[c811,d10]) ).
cnf(d12,plain,
( 'r1$utarski'(sK9(X0,X1),X1)
| ~ 'r2$uhidden'(X1,sK1158)
| ~ 'r2$uclosure3'(sK1156,sK1157,sK1158,X0)
| ~ 'm1$upboole'(sK1157,sK1156)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))) ),
inference(resolution,[status(thm)],[c2,c806]) ).
cnf(d13,plain,
( 'r1$utarski'(sK9(X0,X1),X1)
| ~ 'r2$uhidden'(X1,sK1158)
| ~ 'r2$uclosure3'(sK1156,sK1157,sK1158,X0)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))) ),
inference(resolution,[status(thm)],[c805,d12]) ).
cnf(d14,plain,
( 'r1$utarski'(sK9(sK1159,X0),X0)
| ~ 'r2$uhidden'(X0,sK1158)
| ~ 'r2$uclosure3'(sK1156,sK1157,sK1158,sK1159) ),
inference(resolution,[status(thm)],[d13,c807]) ).
cnf(d15,plain,
( 'r1$utarski'(sK9(sK1159,X0),X0)
| ~ 'r2$uhidden'(X0,sK1158) ),
inference(resolution,[status(thm)],[c809,d14]) ).
cnf(d16,plain,
( ~ 'r2$uhidden'(X1,sK1158)
| ~ 'r2$uhidden'(X0,sK9(sK1159,X1))
| 'r2$uhidden'(X0,X1) ),
inference(resolution,[status(thm)],[c27,d15]) ).
cnf(d17,plain,
( 'r1$utarski'(sK9(X0,X1),X1)
| ~ 'r2$uhidden'(X1,sK1159)
| ~ 'r2$uclosure3'(sK1156,sK1157,sK1159,X0)
| ~ 'm1$upboole'(sK1157,sK1156)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))) ),
inference(resolution,[status(thm)],[c2,c807]) ).
cnf(d18,plain,
( 'r1$utarski'(sK9(X0,X1),X1)
| ~ 'r2$uhidden'(X1,sK1159)
| ~ 'r2$uclosure3'(sK1156,sK1157,sK1159,X0)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))) ),
inference(resolution,[status(thm)],[c805,d17]) ).
cnf(d19,plain,
( 'r1$utarski'(sK9(sK1160,X0),X0)
| ~ 'r2$uhidden'(X0,sK1159)
| ~ 'r2$uclosure3'(sK1156,sK1157,sK1159,sK1160) ),
inference(resolution,[status(thm)],[d18,c808]) ).
cnf(d20,plain,
( 'r1$utarski'(sK9(sK1160,X0),X0)
| ~ 'r2$uhidden'(X0,sK1159) ),
inference(resolution,[status(thm)],[c810,d19]) ).
cnf(d21,plain,
( ~ 'r2$uhidden'(X1,sK1159)
| ~ 'r2$uhidden'(X0,sK9(sK1160,X1))
| 'r2$uhidden'(X0,X1) ),
inference(resolution,[status(thm)],[c27,d20]) ).
cnf(d22,plain,
( 'r2$uhidden'(sK30(sK9(sK1160,X0),X1),X0)
| ~ 'r2$uhidden'(X0,sK1159)
| 'r1$utarski'(sK9(sK1160,X0),X1) ),
inference(resolution,[status(thm)],[c28,d21]) ).
cnf(d23,plain,
( 'r2$uhidden'(sK30(sK9(sK1160,sK9(sK1159,X0)),X1),X0)
| ~ 'r2$uhidden'(X0,sK1158)
| 'r1$utarski'(sK9(sK1160,sK9(sK1159,X0)),X1)
| ~ 'r2$uhidden'(sK9(sK1159,X0),sK1159) ),
inference(resolution,[status(thm)],[d22,d16]) ).
cnf(d24,plain,
( 'r1$utarski'(sK9(sK1160,sK9(sK1159,X0)),X0)
| 'r1$utarski'(sK9(sK1160,sK9(sK1159,X0)),X0)
| ~ 'r2$uhidden'(sK9(sK1159,X0),sK1159)
| ~ 'r2$uhidden'(X0,sK1158) ),
inference(resolution,[status(thm)],[d23,c29]) ).
cnf(d25,plain,
( ~ 'r2$uhidden'(sK9(sK1160,sK9(sK1159,sK10(sK1158,sK1160))),sK1160)
| ~ 'r2$uhidden'(sK9(sK1159,sK10(sK1158,sK1160)),sK1159)
| ~ 'r2$uhidden'(sK10(sK1158,sK1160),sK1158) ),
inference(resolution,[status(thm)],[d24,d11]) ).
cnf(d26,plain,
( 'r2$uhidden'(sK10(X0,sK1160),X0)
| 'r2$uclosure3'(sK1156,sK1157,X0,sK1160)
| ~ 'm1$upboole'(sK1157,sK1156)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))) ),
inference(resolution,[status(thm)],[c3,c808]) ).
cnf(d27,plain,
( 'r2$uhidden'(sK10(X0,sK1160),X0)
| 'r2$uclosure3'(sK1156,sK1157,X0,sK1160)
| ~ 'm1$usubset$u1'(X0,'k1$uzfmisc$u1'('k1$uclosure2'(sK1156,sK1157))) ),
inference(resolution,[status(thm)],[c805,d26]) ).
cnf(d28,plain,
( 'r2$uhidden'(sK10(sK1158,sK1160),sK1158)
| 'r2$uclosure3'(sK1156,sK1157,sK1158,sK1160) ),
inference(resolution,[status(thm)],[d27,c806]) ).
cnf(d29,plain,
'r2$uhidden'(sK10(sK1158,sK1160),sK1158),
inference(resolution,[status(thm)],[c811,d28]) ).
cnf(d30,plain,
( ~ 'r2$uhidden'(sK9(sK1160,sK9(sK1159,sK10(sK1158,sK1160))),sK1160)
| ~ 'r2$uhidden'(sK9(sK1159,sK10(sK1158,sK1160)),sK1159) ),
inference(resolution,[status(thm)],[d29,d25]) ).
cnf(d31,plain,
( ~ 'r2$uhidden'(sK9(sK1159,sK10(sK1158,sK1160)),sK1159)
| ~ 'r2$uhidden'(sK9(sK1159,sK10(sK1158,sK1160)),sK1159) ),
inference(resolution,[status(thm)],[d30,d7]) ).
cnf(d32,plain,
~ 'r2$uhidden'(sK10(sK1158,sK1160),sK1158),
inference(resolution,[status(thm)],[d31,d3]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d29,d32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG224+3 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n026.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 21:37:01 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.64/18.65 % SZS status Theorem for theBenchmark.p
% 38.64/18.65 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------