%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET021-7 : 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 : n020.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 08:31:38 AM UTC 2026
% Result : Unsatisfiable 82.64s 38.87s
% Output : CNFRefutation 82.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of clauses : 19 ( 8 unt; 0 nHn; 19 RR)
% Number of literals : 33 ( 14 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(corollary_2_to_cartesian_product,axiom,
( member(X1,'universal$uclass')
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ) ).
cnf(ordered_pair_determines_components2,axiom,
( X1 = X3
| ~ member(X1,'universal$uclass')
| 'ordered$upair'(X0,X1) != 'ordered$upair'(X2,X3) ) ).
cnf(existence_of_1st_and_2nd_1,axiom,
( member('ordered$upair'(first('ordered$upair'(X0,X1)),second('ordered$upair'(X0,X1))),'cross$uproduct'('universal$uclass','universal$uclass'))
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'('universal$uclass','universal$uclass')) ) ).
cnf(prove_unique_1st_and_2nd_in_pair_of_sets2_1,negated_conjecture,
member('ordered$upair'(u,v),'cross$uproduct'('universal$uclass','universal$uclass')) ).
cnf(prove_unique_1st_and_2nd_in_pair_of_sets2_2,negated_conjecture,
second('ordered$upair'(u,v)) != v ).
cnf(cartesian_product4,axiom,
( 'ordered$upair'(first(X0),second(X0)) = X0
| ~ member(X0,'cross$uproduct'(X1,X2)) ) ).
cnf(c3,plain,
( member(X1,'universal$uclass')
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[corollary_2_to_cartesian_product]) ).
cnf(c60,plain,
( X1 = X3
| ~ member(X1,'universal$uclass')
| 'ordered$upair'(X0,X1) != 'ordered$upair'(X2,X3) ),
inference(clausification,[status(esa)],[ordered_pair_determines_components2]) ).
cnf(c61,plain,
( member('ordered$upair'(first('ordered$upair'(X0,X1)),second('ordered$upair'(X0,X1))),'cross$uproduct'('universal$uclass','universal$uclass'))
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'('universal$uclass','universal$uclass')) ),
inference(clausification,[status(esa)],[existence_of_1st_and_2nd_1]) ).
cnf(c66,plain,
member('ordered$upair'(u,v),'cross$uproduct'('universal$uclass','universal$uclass')),
inference(clausification,[status(esa)],[prove_unique_1st_and_2nd_in_pair_of_sets2_1]) ).
cnf(c67,plain,
second('ordered$upair'(u,v)) != v,
inference(clausification,[status(esa)],[prove_unique_1st_and_2nd_in_pair_of_sets2_2]) ).
cnf(c84,plain,
( 'ordered$upair'(first(X0),second(X0)) = X0
| ~ member(X0,'cross$uproduct'(X1,X2)) ),
inference(clausification,[status(esa)],[cartesian_product4]) ).
cnf(d0,plain,
'ordered$upair'(first('ordered$upair'(u,v)),second('ordered$upair'(u,v))) = 'ordered$upair'(u,v),
inference(resolution,[status(thm)],[c84,c66]) ).
cnf(d1,plain,
( ~ member(second('ordered$upair'(u,v)),'universal$uclass')
| second('ordered$upair'(u,v)) = X1
| 'ordered$upair'(u,v) != 'ordered$upair'(X0,X1) ),
inference(superposition,[status(thm)],[d0,c60]) ).
cnf(d2,plain,
( member(second('ordered$upair'(X0,X1)),'universal$uclass')
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'('universal$uclass','universal$uclass')) ),
inference(resolution,[status(thm)],[c61,c3]) ).
cnf(d3,plain,
member(second('ordered$upair'(u,v)),'universal$uclass'),
inference(resolution,[status(thm)],[d2,c66]) ).
cnf(d4,plain,
( second('ordered$upair'(u,v)) = X1
| 'ordered$upair'(u,v) != 'ordered$upair'(X0,X1) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
second('ordered$upair'(u,v)) = v,
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c67,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET021-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n020.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 06:53:48 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 82.64/38.87 % SZS status Unsatisfiable for theBenchmark.p
% 82.64/38.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------