%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET201-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 08:32:19 AM UTC 2026
% Result : Unsatisfiable 61.32s 29.13s
% Output : CNFRefutation 61.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 39 ( 10 unt; 13 nHn; 29 RR)
% Number of literals : 83 ( 5 equ; 35 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 77 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_intersection_is_monotonic_1,negated_conjecture,
subclass(x,y) ).
cnf(prove_intersection_is_monotonic_2,negated_conjecture,
subclass(z,w) ).
cnf(prove_intersection_is_monotonic_3,negated_conjecture,
~ subclass(intersection(x,z),intersection(y,w)) ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(not_subclass_members1,axiom,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ) ).
cnf(not_subclass_members2,axiom,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ) ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection2,axiom,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection3,axiom,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ) ).
cnf(c0,plain,
subclass(x,y),
inference(clausification,[status(esa)],[prove_intersection_is_monotonic_1]) ).
cnf(c1,plain,
subclass(z,w),
inference(clausification,[status(esa)],[prove_intersection_is_monotonic_2]) ).
cnf(c2,plain,
~ subclass(intersection(x,z),intersection(y,w)),
inference(clausification,[status(esa)],[prove_intersection_is_monotonic_3]) ).
cnf(c3,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c4,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c5,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c9,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c23,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c24,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c25,plain,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(d0,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c24,c4]) ).
cnf(d1,plain,
( member('not$usubclass$uelement'(intersection(X0,X1),X2),X3)
| ~ subclass(X1,X3)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( member('not$usubclass$uelement'(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(d3,plain,
( subclass(X0,intersection(X1,X2))
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X2)
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c25,c5]) ).
cnf(d4,plain,
( subclass(X0,intersection(X1,X2))
| ~ subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,intersection(X1,X2)),X2)
| subclass(X0,intersection(X1,X2)) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( subclass(intersection(X0,X1),intersection(X2,X3))
| ~ subclass(X1,X3)
| subclass(intersection(X0,X1),intersection(X2,X3))
| ~ subclass(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( ~ subclass(intersection(x,z),y)
| ~ subclass(z,w) ),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
~ subclass(intersection(x,z),y),
inference(resolution,[status(thm)],[c1,d6]) ).
cnf(d8,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c23,c4]) ).
cnf(d9,plain,
( member('not$usubclass$uelement'(intersection(intersection(X0,X1),X2),X3),X1)
| subclass(intersection(intersection(X0,X1),X2),X3) ),
inference(resolution,[status(thm)],[d8,c24]) ).
cnf(d10,plain,
( subclass(intersection(intersection(X0,X1),X2),X1)
| subclass(intersection(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[d9,c5]) ).
cnf(d11,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d8,c5]) ).
cnf(d12,plain,
( ~ subclass(X0,intersection(X0,X1))
| X0 = intersection(X0,X1) ),
inference(resolution,[status(thm)],[d11,c9]) ).
cnf(d13,plain,
( subclass(X0,intersection(X0,X1))
| ~ member('not$usubclass$uelement'(X0,intersection(X0,X1)),X1)
| subclass(X0,intersection(X0,X1)) ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d14,plain,
( subclass(X0,intersection(X0,X1))
| ~ subclass(X0,X1)
| subclass(X0,intersection(X0,X1)) ),
inference(resolution,[status(thm)],[d13,d2]) ).
cnf(d15,plain,
( X0 = intersection(X0,X1)
| ~ subclass(X0,X1) ),
inference(resolution,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
x = intersection(x,y),
inference(resolution,[status(thm)],[d15,c0]) ).
cnf(d17,plain,
subclass(intersection(x,X0),y),
inference(superposition,[status(thm)],[d16,d10]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET201-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n015.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 07:22:43 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.32/29.13 % SZS status Unsatisfiable for theBenchmark.p
% 61.32/29.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------