%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LAT291+1 : 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 : n018.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 07:48:08 AM UTC 2026
% Result : Theorem 21.10s 3.26s
% Output : CNFRefutation 21.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 14 unt; 0 def)
% Number of atoms : 142 ( 31 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 161 ( 61 ~; 71 |; 21 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-4 aty)
% Number of variables : 17 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(dt_k5_lattices,axiom,
! [X0] :
( ( 'l1$ulattices'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> 'm1$usubset$u1'('k5$ulattices'(X0),'u1$ustruct$u0'(X0)) ) ).
fof(dt_l3_lattices,axiom,
! [X0] :
( 'l3$ulattices'(X0)
=> ( 'l2$ulattices'(X0)
& 'l1$ulattices'(X0) ) ) ).
fof(t28_lopclset,axiom,
! [X0] :
( ( 'l3$ulattices'(X0)
& ~ 'v3$urealset2'(X0)
& 'v17$ulattices'(X0)
& 'v10$ulattices'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> ! [X1] :
( 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
=> 'k4$uxboole$u0'('k7$ulopclset'(X0),'k8$ufunct$u2'('u1$ustruct$u0'(X0),'k1$uzfmisc$u1'('k7$ulopclset'(X0)),'k9$ulopclset'(X0),X1)) = 'k8$ufunct$u2'('u1$ustruct$u0'(X0),'k1$uzfmisc$u1'('k7$ulopclset'(X0)),'k9$ulopclset'(X0),'k7$ulattices'(X0,X1)) ) ) ).
fof(t36_lopclset,axiom,
! [X0] :
( ( 'l3$ulattices'(X0)
& ~ 'v3$urealset2'(X0)
& 'v17$ulattices'(X0)
& 'v10$ulattices'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> 'k8$ufunct$u2'('u1$ustruct$u0'(X0),'k1$uzfmisc$u1'('k7$ulopclset'(X0)),'k9$ulopclset'(X0),'k5$ulattices'(X0)) = 'k1$uxboole$u0' ) ).
fof(t37_lattice4,axiom,
! [X0] :
( ( 'l3$ulattices'(X0)
& 'v17$ulattices'(X0)
& 'v10$ulattices'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> 'k7$ulattices'(X0,'k5$ulattices'(X0)) = 'k6$ulattices'(X0) ) ).
fof(t3_boole,axiom,
! [X0] : 'k4$uxboole$u0'(X0,'k1$uxboole$u0') = X0 ).
fof(t37_lopclset,conjecture,
! [X0] :
( ( 'l3$ulattices'(X0)
& ~ 'v3$urealset2'(X0)
& 'v17$ulattices'(X0)
& 'v10$ulattices'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> 'k8$ufunct$u2'('u1$ustruct$u0'(X0),'k1$uzfmisc$u1'('k7$ulopclset'(X0)),'k9$ulopclset'(X0),'k6$ulattices'(X0)) = 'k7$ulopclset'(X0) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ( 'l3$ulattices'(X0)
& ~ 'v3$urealset2'(X0)
& 'v17$ulattices'(X0)
& 'v10$ulattices'(X0)
& ~ 'v3$ustruct$u0'(X0) )
=> 'k8$ufunct$u2'('u1$ustruct$u0'(X0),'k1$uzfmisc$u1'('k7$ulopclset'(X0)),'k9$ulopclset'(X0),'k6$ulattices'(X0)) = 'k7$ulopclset'(X0) ),
inference(negate_conjecture,[status(cth)],[t37_lopclset]) ).
cnf(c93,plain,
( 'm1$usubset$u1'('k5$ulattices'(X0),'u1$ustruct$u0'(X0))
| ~ 'l1$ulattices'(X0)
| 'v3$ustruct$u0'(X0) ),
inference(clausification,[status(esa)],[dt_k5_lattices]) ).
cnf(c105,plain,
( 'l1$ulattices'(X0)
| ~ 'l3$ulattices'(X0) ),
inference(clausification,[status(esa)],[dt_l3_lattices]) ).
cnf(c200,plain,
( ~ 'l3$ulattices'(X0)
| ~ 'v17$ulattices'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'm1$usubset$u1'(X1,'u1$ustruct$u0'(X0))
| ~ 'v10$ulattices'(X0)
| 'v3$urealset2'(X0)
| 'k4$uxboole$u0'('k7$ulopclset'(X0),'k8$ufunct$u2'('u1$ustruct$u0'(X0),'k1$uzfmisc$u1'('k7$ulopclset'(X0)),'k9$ulopclset'(X0),X1)) = 'k8$ufunct$u2'('u1$ustruct$u0'(X0),'k1$uzfmisc$u1'('k7$ulopclset'(X0)),'k9$ulopclset'(X0),'k7$ulattices'(X0,X1)) ),
inference(clausification,[status(esa)],[t28_lopclset]) ).
cnf(c206,plain,
( ~ 'v17$ulattices'(X0)
| 'v3$ustruct$u0'(X0)
| 'v3$urealset2'(X0)
| ~ 'l3$ulattices'(X0)
| ~ 'v10$ulattices'(X0)
| 'k8$ufunct$u2'('u1$ustruct$u0'(X0),'k1$uzfmisc$u1'('k7$ulopclset'(X0)),'k9$ulopclset'(X0),'k5$ulattices'(X0)) = 'k1$uxboole$u0' ),
inference(clausification,[status(esa)],[t36_lopclset]) ).
cnf(c207,plain,
( ~ 'v10$ulattices'(X0)
| ~ 'l3$ulattices'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'v17$ulattices'(X0)
| 'k7$ulattices'(X0,'k5$ulattices'(X0)) = 'k6$ulattices'(X0) ),
inference(clausification,[status(esa)],[t37_lattice4]) ).
cnf(c208,plain,
'k4$uxboole$u0'(X0,'k1$uxboole$u0') = X0,
inference(clausification,[status(esa)],[t3_boole]) ).
cnf(c217,plain,
~ 'v3$ustruct$u0'(sK165),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
'v10$ulattices'(sK165),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
'v17$ulattices'(sK165),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
~ 'v3$urealset2'(sK165),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c221,plain,
'l3$ulattices'(sK165),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c222,plain,
'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k6$ulattices'(sK165)) != 'k7$ulopclset'(sK165),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'v3$ustruct$u0'(sK165)
| ~ 'v10$ulattices'(sK165)
| ~ 'l3$ulattices'(sK165)
| 'k7$ulattices'(sK165,'k5$ulattices'(sK165)) = 'k6$ulattices'(sK165) ),
inference(resolution,[status(thm)],[c207,c219]) ).
cnf(d1,plain,
( ~ 'v10$ulattices'(sK165)
| ~ 'l3$ulattices'(sK165)
| 'k7$ulattices'(sK165,'k5$ulattices'(sK165)) = 'k6$ulattices'(sK165) ),
inference(resolution,[status(thm)],[c217,d0]) ).
cnf(d2,plain,
( ~ 'l3$ulattices'(sK165)
| 'k7$ulattices'(sK165,'k5$ulattices'(sK165)) = 'k6$ulattices'(sK165) ),
inference(resolution,[status(thm)],[c218,d1]) ).
cnf(d3,plain,
'k7$ulattices'(sK165,'k5$ulattices'(sK165)) = 'k6$ulattices'(sK165),
inference(resolution,[status(thm)],[c221,d2]) ).
cnf(d4,plain,
( 'v3$urealset2'(sK165)
| 'v3$ustruct$u0'(sK165)
| ~ 'v10$ulattices'(sK165)
| ~ 'l3$ulattices'(sK165)
| 'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k5$ulattices'(sK165)) = 'k1$uxboole$u0' ),
inference(resolution,[status(thm)],[c206,c219]) ).
cnf(d5,plain,
( 'v3$urealset2'(sK165)
| ~ 'v10$ulattices'(sK165)
| ~ 'l3$ulattices'(sK165)
| 'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k5$ulattices'(sK165)) = 'k1$uxboole$u0' ),
inference(resolution,[status(thm)],[c217,d4]) ).
cnf(d6,plain,
( 'v3$urealset2'(sK165)
| ~ 'l3$ulattices'(sK165)
| 'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k5$ulattices'(sK165)) = 'k1$uxboole$u0' ),
inference(resolution,[status(thm)],[c218,d5]) ).
cnf(d7,plain,
( ~ 'l3$ulattices'(sK165)
| 'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k5$ulattices'(sK165)) = 'k1$uxboole$u0' ),
inference(resolution,[status(thm)],[c220,d6]) ).
cnf(d8,plain,
'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k5$ulattices'(sK165)) = 'k1$uxboole$u0',
inference(resolution,[status(thm)],[c221,d7]) ).
cnf(d9,plain,
'l1$ulattices'(sK165),
inference(resolution,[status(thm)],[c105,c221]) ).
cnf(d10,plain,
( ~ 'l1$ulattices'(X0)
| 'v3$ustruct$u0'(X0)
| 'v3$urealset2'(X0)
| ~ 'v17$ulattices'(X0)
| 'v3$ustruct$u0'(X0)
| ~ 'v10$ulattices'(X0)
| ~ 'l3$ulattices'(X0)
| 'k4$uxboole$u0'('k7$ulopclset'(X0),'k8$ufunct$u2'('u1$ustruct$u0'(X0),'k1$uzfmisc$u1'('k7$ulopclset'(X0)),'k9$ulopclset'(X0),'k5$ulattices'(X0))) = 'k8$ufunct$u2'('u1$ustruct$u0'(X0),'k1$uzfmisc$u1'('k7$ulopclset'(X0)),'k9$ulopclset'(X0),'k7$ulattices'(X0,'k5$ulattices'(X0))) ),
inference(resolution,[status(thm)],[c200,c93]) ).
cnf(d11,plain,
( 'v3$urealset2'(sK165)
| ~ 'v17$ulattices'(sK165)
| 'v3$ustruct$u0'(sK165)
| ~ 'v10$ulattices'(sK165)
| ~ 'l3$ulattices'(sK165)
| 'k4$uxboole$u0'('k7$ulopclset'(sK165),'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k5$ulattices'(sK165))) = 'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k7$ulattices'(sK165,'k5$ulattices'(sK165))) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( 'v3$urealset2'(sK165)
| ~ 'v17$ulattices'(sK165)
| 'v3$ustruct$u0'(sK165)
| ~ 'v10$ulattices'(sK165)
| ~ 'l3$ulattices'(sK165)
| 'k4$uxboole$u0'('k7$ulopclset'(sK165),'k1$uxboole$u0') = 'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k7$ulattices'(sK165,'k5$ulattices'(sK165))) ),
inference(demodulation,[status(thm)],[d11,d8]) ).
cnf(d13,plain,
( 'v3$urealset2'(sK165)
| ~ 'v17$ulattices'(sK165)
| 'v3$ustruct$u0'(sK165)
| ~ 'v10$ulattices'(sK165)
| ~ 'l3$ulattices'(sK165)
| 'k7$ulopclset'(sK165) = 'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k7$ulattices'(sK165,'k5$ulattices'(sK165))) ),
inference(demodulation,[status(thm)],[d12,c208]) ).
cnf(d14,plain,
( 'v3$urealset2'(sK165)
| ~ 'v17$ulattices'(sK165)
| 'v3$ustruct$u0'(sK165)
| ~ 'v10$ulattices'(sK165)
| ~ 'l3$ulattices'(sK165)
| 'k7$ulopclset'(sK165) = 'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k6$ulattices'(sK165)) ),
inference(demodulation,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
( 'v3$urealset2'(sK165)
| ~ 'v17$ulattices'(sK165)
| ~ 'v10$ulattices'(sK165)
| ~ 'l3$ulattices'(sK165)
| 'k7$ulopclset'(sK165) = 'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k6$ulattices'(sK165)) ),
inference(resolution,[status(thm)],[c217,d14]) ).
cnf(d16,plain,
( 'v3$urealset2'(sK165)
| ~ 'v17$ulattices'(sK165)
| ~ 'l3$ulattices'(sK165)
| 'k7$ulopclset'(sK165) = 'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k6$ulattices'(sK165)) ),
inference(resolution,[status(thm)],[c218,d15]) ).
cnf(d17,plain,
( 'v3$urealset2'(sK165)
| ~ 'l3$ulattices'(sK165)
| 'k7$ulopclset'(sK165) = 'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k6$ulattices'(sK165)) ),
inference(resolution,[status(thm)],[c219,d16]) ).
cnf(d18,plain,
( ~ 'l3$ulattices'(sK165)
| 'k7$ulopclset'(sK165) = 'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k6$ulattices'(sK165)) ),
inference(resolution,[status(thm)],[c220,d17]) ).
cnf(d19,plain,
'k7$ulopclset'(sK165) = 'k8$ufunct$u2'('u1$ustruct$u0'(sK165),'k1$uzfmisc$u1'('k7$ulopclset'(sK165)),'k9$ulopclset'(sK165),'k6$ulattices'(sK165)),
inference(resolution,[status(thm)],[c221,d18]) ).
cnf(d20,plain,
'k7$ulopclset'(sK165) != 'k7$ulopclset'(sK165),
inference(demodulation,[status(thm)],[c222,d19]) ).
cnf(d21,plain,
$false,
inference(equality_resolution,[status(thm)],[d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT291+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.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 : Fri Sep 25 20:32:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.10/3.26 % SZS status Theorem for theBenchmark.p
% 21.10/3.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------