%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET974+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 08:33:39 AM UTC 2026
% Result : Theorem 18.34s 8.16s
% Output : CNFRefutation 18.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 7 unt; 0 def)
% Number of atoms : 47 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 44 ( 21 ~; 14 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 62 ( 11 sgn 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k3_xboole_0,axiom,
! [X0,X1] : 'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0) ).
fof(symmetry_r1_xboole_0,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ) ).
fof(t104_zfmisc_1,axiom,
! [X0,X1,X2,X3,X4] :
~ ( ! [X5,X6] :
~ ( in(X6,'set$uintersection2'(X2,X4))
& in(X5,'set$uintersection2'(X1,X3))
& X0 = 'ordered$upair'(X5,X6) )
& in(X0,'set$uintersection2'('cartesian$uproduct2'(X1,X2),'cartesian$uproduct2'(X3,X4))) ) ).
fof(t4_xboole_0,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,'set$uintersection2'(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,'set$uintersection2'(X0,X1))
& ~ disjoint(X0,X1) ) ) ).
fof(t127_zfmisc_1,conjecture,
! [X0,X1,X2,X3] :
( ( disjoint(X2,X3)
| disjoint(X0,X1) )
=> disjoint('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X3)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( disjoint(X2,X3)
| disjoint(X0,X1) )
=> disjoint('cartesian$uproduct2'(X0,X2),'cartesian$uproduct2'(X1,X3)) ),
inference(negate_conjecture,[status(cth)],[t127_zfmisc_1]) ).
cnf(c2,plain,
'set$uintersection2'(X0,X1) = 'set$uintersection2'(X1,X0),
inference(clausification,[status(esa)],[commutativity_k3_xboole_0]) ).
cnf(c8,plain,
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_r1_xboole_0]) ).
cnf(c10,plain,
( in(sK21(X0,X1,X2,X3,X4),'set$uintersection2'(X1,X3))
| ~ in(X0,'set$uintersection2'('cartesian$uproduct2'(X1,X2),'cartesian$uproduct2'(X3,X4))) ),
inference(clausification,[status(esa)],[t104_zfmisc_1]) ).
cnf(c11,plain,
( in(sK22(X0,X1,X2,X3,X4),'set$uintersection2'(X2,X4))
| ~ in(X0,'set$uintersection2'('cartesian$uproduct2'(X1,X2),'cartesian$uproduct2'(X3,X4))) ),
inference(clausification,[status(esa)],[t104_zfmisc_1]) ).
cnf(c12,plain,
( in(sK25(X0,X1),'set$uintersection2'(X0,X1))
| disjoint(X0,X1) ),
inference(clausification,[status(esa)],[t4_xboole_0]) ).
cnf(c13,plain,
( ~ disjoint(X1,X2)
| ~ in(X0,'set$uintersection2'(X1,X2)) ),
inference(clausification,[status(esa)],[t4_xboole_0]) ).
cnf(c14,plain,
( disjoint(sK29,sK30)
| disjoint(sK27,sK28) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
~ disjoint('cartesian$uproduct2'(sK27,sK29),'cartesian$uproduct2'(sK28,sK30)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( disjoint(X0,X1)
| in(sK25(X0,X1),'set$uintersection2'(X1,X0)) ),
inference(superposition,[status(thm)],[c2,c12]) ).
cnf(d1,plain,
( ~ in(X2,'set$uintersection2'('cartesian$uproduct2'(X0,X3),'cartesian$uproduct2'(X1,X4)))
| ~ disjoint(X0,X1) ),
inference(resolution,[status(thm)],[c13,c10]) ).
cnf(d2,plain,
( disjoint('cartesian$uproduct2'(X1,X2),'cartesian$uproduct2'(X0,X3))
| ~ disjoint(X0,X1) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
~ disjoint(sK28,sK27),
inference(resolution,[status(thm)],[d2,c15]) ).
cnf(d4,plain,
( disjoint(sK29,sK30)
| disjoint(sK28,sK27) ),
inference(resolution,[status(thm)],[c8,c14]) ).
cnf(d5,plain,
( ~ in(X2,'set$uintersection2'('cartesian$uproduct2'(X3,X0),'cartesian$uproduct2'(X4,X1)))
| ~ disjoint(X0,X1) ),
inference(resolution,[status(thm)],[c13,c11]) ).
cnf(d6,plain,
( disjoint('cartesian$uproduct2'(X2,X0),'cartesian$uproduct2'(X3,X1))
| ~ disjoint(X0,X1) ),
inference(resolution,[status(thm)],[d5,c12]) ).
cnf(d7,plain,
~ disjoint(sK29,sK30),
inference(resolution,[status(thm)],[d6,c15]) ).
cnf(d8,plain,
disjoint(sK28,sK27),
inference(resolution,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET974+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/5.45 % Computer : n016.cluster.edu
% 0.19/5.45 % Model : x86_64 x86_64
% 0.19/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.45 % Memory : 8046.5625MB
% 0.19/5.45 % OS : Linux 6.8.0-71-generic
% 0.19/5.45 % CPULimit : 300
% 0.19/5.45 % WCLimit : 300
% 0.19/5.45 % DateTime : Sat Sep 26 08:33:22 UTC 2026
% 0.19/5.45 % CPUTime :
% 0.19/5.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.34/8.16 % SZS status Theorem for theBenchmark.p
% 18.34/8.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------