%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET052-6 : 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 : n003.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 08:31:46 AM UTC 2026
% Result : Unsatisfiable 23.13s 13.42s
% Output : CNFRefutation 23.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 9 unt; 0 nHn; 12 RR)
% Number of literals : 21 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 18 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_corollary_1_to_cartesian_product_1,negated_conjecture,
member('ordered$upair'(u,v),'cross$uproduct'(x,y)) ).
cnf(prove_corollary_1_to_cartesian_product_2,negated_conjecture,
~ member(u,'universal$uclass') ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(class_elements_are_sets,axiom,
subclass(X0,'universal$uclass') ).
cnf(cartesian_product1,axiom,
( member(X0,X2)
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ) ).
cnf(c0,plain,
member('ordered$upair'(u,v),'cross$uproduct'(x,y)),
inference(clausification,[status(esa)],[prove_corollary_1_to_cartesian_product_1]) ).
cnf(c1,plain,
~ member(u,'universal$uclass'),
inference(clausification,[status(esa)],[prove_corollary_1_to_cartesian_product_2]) ).
cnf(c2,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c5,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c15,plain,
( member(X0,X2)
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[cartesian_product1]) ).
cnf(d0,plain,
member(u,x),
inference(resolution,[status(thm)],[c15,c0]) ).
cnf(d1,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c2,c5]) ).
cnf(d2,plain,
member(u,'universal$uclass'),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c1,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET052-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/10.43 % Computer : n003.cluster.edu
% 0.18/10.43 % Model : x86_64 x86_64
% 0.18/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/10.43 % Memory : 8046.5625MB
% 0.18/10.43 % OS : Linux 6.8.0-71-generic
% 0.18/10.43 % CPULimit : 300
% 0.18/10.43 % WCLimit : 300
% 0.18/10.43 % DateTime : Sat Sep 26 07:01:49 UTC 2026
% 0.18/10.44 % CPUTime :
% 0.18/10.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.13/13.42 % SZS status Unsatisfiable for theBenchmark.p
% 23.13/13.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------