%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET454-6 : 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 : n004.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 08:32:38 AM UTC 2026
% Result : Unsatisfiable 30.30s 4.41s
% Output : CNFRefutation 16.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 30 ( 14 unt; 7 nHn; 21 RR)
% Number of literals : 50 ( 8 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 45 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_identity_alternate_defn1_1,negated_conjecture,
~ subclass('identity$urelation','cross$uproduct'('universal$uclass','universal$uclass')) ).
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(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection2,axiom,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(restriction2,axiom,
intersection('cross$uproduct'(X0,X1),X2) = restrict(X2,X0,X1) ).
cnf(subset_relation,axiom,
intersection('cross$uproduct'('universal$uclass','universal$uclass'),intersection('cross$uproduct'('universal$uclass','universal$uclass'),complement(compose(complement('element$urelation'),inverse('element$urelation'))))) = 'subset$urelation' ).
cnf(identity_relation,axiom,
intersection(inverse('subset$urelation'),'subset$urelation') = 'identity$urelation' ).
cnf(c0,plain,
~ subclass('identity$urelation','cross$uproduct'('universal$uclass','universal$uclass')),
inference(clausification,[status(esa)],[prove_identity_alternate_defn1_1]) ).
cnf(c1,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c2,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c3,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c21,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c22,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c29,plain,
intersection('cross$uproduct'(X0,X1),X2) = restrict(X2,X0,X1),
inference(clausification,[status(esa)],[restriction2]) ).
cnf(c74,plain,
intersection('cross$uproduct'('universal$uclass','universal$uclass'),intersection('cross$uproduct'('universal$uclass','universal$uclass'),complement(compose(complement('element$urelation'),inverse('element$urelation'))))) = 'subset$urelation',
inference(clausification,[status(esa)],[subset_relation]) ).
cnf(c75,plain,
intersection(inverse('subset$urelation'),'subset$urelation') = 'identity$urelation',
inference(clausification,[status(esa)],[identity_relation]) ).
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(restrict(X2,X0,X1),'cross$uproduct'(X0,X1)),
inference(superposition,[status(thm)],[c29,d1]) ).
cnf(d3,plain,
restrict(intersection('cross$uproduct'('universal$uclass','universal$uclass'),complement(compose(complement('element$urelation'),inverse('element$urelation')))),'universal$uclass','universal$uclass') = 'subset$urelation',
inference(demodulation,[status(thm)],[c74,c29]) ).
cnf(d4,plain,
restrict(restrict(complement(compose(complement('element$urelation'),inverse('element$urelation'))),'universal$uclass','universal$uclass'),'universal$uclass','universal$uclass') = 'subset$urelation',
inference(demodulation,[status(thm)],[d3,c29]) ).
cnf(d5,plain,
subclass('subset$urelation','cross$uproduct'('universal$uclass','universal$uclass')),
inference(superposition,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( member(X0,'subset$urelation')
| ~ member(X0,'identity$urelation') ),
inference(superposition,[status(thm)],[c75,c22]) ).
cnf(d7,plain,
( subclass('identity$urelation',X0)
| member('not$usubclass$uelement'('identity$urelation',X0),'subset$urelation') ),
inference(resolution,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
( member('not$usubclass$uelement'('identity$urelation',X0),X1)
| ~ subclass('subset$urelation',X1)
| subclass('identity$urelation',X0) ),
inference(resolution,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
( subclass('identity$urelation',X0)
| ~ subclass('subset$urelation',X0)
| subclass('identity$urelation',X0) ),
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
subclass('identity$urelation','cross$uproduct'('universal$uclass','universal$uclass')),
inference(resolution,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c0,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET454-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 07:45:06 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.30/4.41 % SZS status Unsatisfiable for theBenchmark.p
% 30.30/4.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------