%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET630+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 : n007.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 10.56s 1.96s
% Output : CNFRefutation 10.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 31 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 9 ~; 8 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [X0,X1] : 'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)) ).
fof(intersect_with_union,axiom,
! [X0,X1,X2] :
( intersect(X0,union(X1,X2))
<=> ( intersect(X0,X2)
| intersect(X0,X1) ) ) ).
fof(intersection_and_union_disjoint,axiom,
! [X0,X1] : disjoint(intersection(X0,X1),difference(X0,X1)) ).
fof(disjoint_defn,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ) ).
fof(commutativity_of_intersection,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0) ).
fof(prove_intersection_and_symmetric_difference_disjoint,conjecture,
! [X0,X1] : disjoint(intersection(X0,X1),'symmetric$udifference'(X0,X1)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : disjoint(intersection(X0,X1),'symmetric$udifference'(X0,X1)),
inference(negate_conjecture,[status(cth)],[prove_intersection_and_symmetric_difference_disjoint]) ).
cnf(c0,plain,
'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(clausification,[status(esa)],[symmetric_difference_defn]) ).
cnf(c1,plain,
( intersect(X0,X2)
| intersect(X0,X1)
| ~ intersect(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[intersect_with_union]) ).
cnf(c4,plain,
disjoint(intersection(X0,X1),difference(X0,X1)),
inference(clausification,[status(esa)],[intersection_and_union_disjoint]) ).
cnf(c11,plain,
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(clausification,[status(esa)],[disjoint_defn]) ).
cnf(c12,plain,
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(clausification,[status(esa)],[disjoint_defn]) ).
cnf(c14,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_intersection]) ).
cnf(c23,plain,
~ disjoint(intersection(sK28,sK29),'symmetric$udifference'(sK28,sK29)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
intersect(intersection(sK28,sK29),'symmetric$udifference'(sK28,sK29)),
inference(resolution,[status(thm)],[c12,c23]) ).
cnf(d1,plain,
( intersect(X2,difference(X0,X1))
| intersect(X2,difference(X1,X0))
| ~ intersect(X2,'symmetric$udifference'(X0,X1)) ),
inference(superposition,[status(thm)],[c0,c1]) ).
cnf(d2,plain,
( intersect(intersection(sK28,sK29),difference(sK28,sK29))
| intersect(intersection(sK28,sK29),difference(sK29,sK28)) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
~ intersect(intersection(X0,X1),difference(X0,X1)),
inference(resolution,[status(thm)],[c4,c11]) ).
cnf(d4,plain,
intersect(intersection(sK28,sK29),difference(sK29,sK28)),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
~ intersect(intersection(X1,X0),difference(X0,X1)),
inference(superposition,[status(thm)],[c14,d3]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET630+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 07:59:39 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.56/1.96 % SZS status Theorem for theBenchmark.p
% 10.56/1.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------