%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET236-6 : 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 : n002.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 08:32:22 AM UTC 2026
% Result : Unsatisfiable 28.42s 13.71s
% Output : CNFRefutation 28.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 9 unt; 4 nHn; 18 RR)
% Number of literals : 37 ( 2 equ; 14 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_cross_product_property11_1,negated_conjecture,
subclass(x,'cross$uproduct'('universal$uclass','universal$uclass')) ).
cnf(prove_cross_product_property11_2,negated_conjecture,
member('ordered$upair'(first('not$usubclass$uelement'(x,y)),second('not$usubclass$uelement'(x,y))),y) ).
cnf(prove_cross_product_property11_3,negated_conjecture,
~ subclass(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(cartesian_product4,axiom,
( 'ordered$upair'(first(X0),second(X0)) = X0
| ~ member(X0,'cross$uproduct'(X1,X2)) ) ).
cnf(c0,plain,
subclass(x,'cross$uproduct'('universal$uclass','universal$uclass')),
inference(clausification,[status(esa)],[prove_cross_product_property11_1]) ).
cnf(c1,plain,
member('ordered$upair'(first('not$usubclass$uelement'(x,y)),second('not$usubclass$uelement'(x,y))),y),
inference(clausification,[status(esa)],[prove_cross_product_property11_2]) ).
cnf(c2,plain,
~ subclass(x,y),
inference(clausification,[status(esa)],[prove_cross_product_property11_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(c19,plain,
( 'ordered$upair'(first(X0),second(X0)) = X0
| ~ member(X0,'cross$uproduct'(X1,X2)) ),
inference(clausification,[status(esa)],[cartesian_product4]) ).
cnf(d0,plain,
( member('not$usubclass$uelement'(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[c4,c3]) ).
cnf(d1,plain,
( ~ member('not$usubclass$uelement'(x,y),'cross$uproduct'(X0,X1))
| member('not$usubclass$uelement'(x,y),y) ),
inference(superposition,[status(thm)],[c19,c1]) ).
cnf(d2,plain,
( subclass(x,y)
| ~ subclass(x,'cross$uproduct'(X0,X1))
| member('not$usubclass$uelement'(x,y),y) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
( member('not$usubclass$uelement'(x,y),y)
| ~ subclass(x,'cross$uproduct'(X0,X1)) ),
inference(resolution,[status(thm)],[c2,d2]) ).
cnf(d4,plain,
member('not$usubclass$uelement'(x,y),y),
inference(resolution,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
subclass(x,y),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c2,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET236-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n002.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Sat Sep 26 07:25:07 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.42/13.71 % SZS status Unsatisfiable for theBenchmark.p
% 28.42/13.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------