%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET629+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 08:32:57 AM UTC 2026
% Result : Theorem 10.95s 1.78s
% Output : CNFRefutation 10.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 6 unt; 0 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 15 ~; 9 |; 3 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 2 sgn 16 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ) ).
fof(difference_defn,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ) ).
fof(intersect_defn,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ) ).
fof(disjoint_defn,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ) ).
fof(symmetry_of_intersect,axiom,
! [X0,X1] :
( intersect(X0,X1)
=> intersect(X1,X0) ) ).
fof(prove_intersection_and_difference_disjoint,conjecture,
! [X0,X1] : disjoint(intersection(X0,X1),difference(X0,X1)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : disjoint(intersection(X0,X1),difference(X0,X1)),
inference(negate_conjecture,[status(cth)],[prove_intersection_and_difference_disjoint]) ).
cnf(c1,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c4,plain,
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c6,plain,
( member(sK8(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c7,plain,
( member(sK8(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c10,plain,
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(clausification,[status(esa)],[disjoint_defn]) ).
cnf(c12,plain,
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_intersect]) ).
cnf(c19,plain,
~ disjoint(intersection(sK20,sK21),difference(sK20,sK21)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
intersect(intersection(sK20,sK21),difference(sK20,sK21)),
inference(resolution,[status(thm)],[c10,c19]) ).
cnf(d1,plain,
intersect(difference(sK20,sK21),intersection(sK20,sK21)),
inference(resolution,[status(thm)],[c12,d0]) ).
cnf(d2,plain,
( ~ member(sK8(difference(X0,X1),X2),X1)
| ~ intersect(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c6,c4]) ).
cnf(d3,plain,
( member(sK8(X0,intersection(X1,X2)),X2)
| ~ intersect(X0,intersection(X1,X2)) ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d4,plain,
( ~ intersect(difference(X0,X1),intersection(X2,X1))
| ~ intersect(difference(X0,X1),intersection(X2,X1)) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET629+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:04:59 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.95/1.78 % SZS status Theorem for theBenchmark.p
% 10.95/1.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------