%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET149-6 : 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 : n006.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 08:32:11 AM UTC 2026
% Result : Unsatisfiable 37.94s 22.17s
% Output : CNFRefutation 37.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of clauses : 28 ( 4 unt; 9 nHn; 20 RR)
% Number of literals : 63 ( 7 equ; 28 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_corollary_to_idempotency_of_intersection_1,negated_conjecture,
intersection(x,intersection(x,y)) != intersection(x,y) ).
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,
intersection(x,intersection(x,y)) != intersection(x,y),
inference(clausification,[status(esa)],[prove_corollary_to_idempotency_of_intersection_1]) ).
cnf(c1,plain,
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c2,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c3,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c7,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c21,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c22,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c23,plain,
( member(X0,intersection(X2,X1))
| ~ 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),X0) ),
inference(resolution,[status(thm)],[c21,c2]) ).
cnf(d1,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c22,c2]) ).
cnf(d3,plain,
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( ~ subclass(X1,intersection(X0,X1))
| intersection(X0,X1) = X1 ),
inference(resolution,[status(thm)],[d3,c7]) ).
cnf(d5,plain,
( member('not$usubclass$uelement'(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(d6,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)],[c23,c3]) ).
cnf(d7,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)],[d6,d5]) ).
cnf(d8,plain,
( subclass(X0,intersection(X1,X0))
| subclass(X0,intersection(X1,X0))
| ~ subclass(X0,X1) ),
inference(resolution,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
( intersection(X1,X0) = X0
| ~ subclass(X0,X1) ),
inference(resolution,[status(thm)],[d8,d4]) ).
cnf(d10,plain,
intersection(X0,intersection(X0,X1)) = intersection(X0,X1),
inference(resolution,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET149-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n006.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 07:13:25 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.94/22.17 % SZS status Unsatisfiable for theBenchmark.p
% 37.94/22.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------