%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET027-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:31:41 AM UTC 2026
% Result : Unsatisfiable 23.20s 5.53s
% Output : CNFRefutation 23.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 9 unt; 10 nHn; 27 RR)
% Number of literals : 69 ( 4 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_transitivity_of_subclass_1,negated_conjecture,
subclass(x,y) ).
cnf(prove_transitivity_of_subclass_2,negated_conjecture,
subclass(y,z) ).
cnf(prove_transitivity_of_subclass_3,negated_conjecture,
~ subclass(x,z) ).
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(c5,plain,
subclass(x,y),
inference(clausification,[status(esa)],[prove_transitivity_of_subclass_1]) ).
cnf(c6,plain,
subclass(y,z),
inference(clausification,[status(esa)],[prove_transitivity_of_subclass_2]) ).
cnf(c7,plain,
~ subclass(x,z),
inference(clausification,[status(esa)],[prove_transitivity_of_subclass_3]) ).
cnf(c8,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c9,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c10,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c14,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c28,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c29,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c30,plain,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(d0,plain,
( ~ member(X0,y)
| member(X0,z) ),
inference(resolution,[status(thm)],[c8,c6]) ).
cnf(d1,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c29,c9]) ).
cnf(d2,plain,
( member('not$usubclass$uelement'(intersection(X0,y),X1),z)
| subclass(intersection(X0,y),X1) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( subclass(intersection(X0,y),z)
| subclass(intersection(X0,y),z) ),
inference(resolution,[status(thm)],[d2,c10]) ).
cnf(d4,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c28,c9]) ).
cnf(d5,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d4,c10]) ).
cnf(d6,plain,
( ~ subclass(X0,intersection(X0,X1))
| intersection(X0,X1) = X0 ),
inference(resolution,[status(thm)],[d5,c14]) ).
cnf(d7,plain,
( ~ member(X0,x)
| member(X0,y) ),
inference(resolution,[status(thm)],[c8,c5]) ).
cnf(d8,plain,
( subclass(x,X0)
| member('not$usubclass$uelement'(x,X0),y) ),
inference(resolution,[status(thm)],[d7,c9]) ).
cnf(d9,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)],[c30,c10]) ).
cnf(d10,plain,
( subclass(X0,intersection(X0,X1))
| subclass(X0,intersection(X0,X1))
| ~ member('not$usubclass$uelement'(X0,intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[d9,c9]) ).
cnf(d11,plain,
( subclass(x,intersection(x,y))
| subclass(x,intersection(x,y)) ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
intersection(x,y) = x,
inference(resolution,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
subclass(x,z),
inference(superposition,[status(thm)],[d12,d3]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[c7,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET027-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n009.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 06:54:59 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.20/5.53 % SZS status Unsatisfiable for theBenchmark.p
% 23.20/5.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------