%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET021-6 : 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 : n019.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 72.04s 42.37s
% Output : CNFRefutation 72.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 31 ( 16 unt; 3 nHn; 26 RR)
% Number of literals : 51 ( 15 equ; 20 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 : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
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$upair'(u,v)) != v ).
cnf(unordered_pair_member,axiom,
( X0 = X2
| X0 = X1
| ~ member(X0,'unordered$upair'(X1,X2)) ) ).
cnf(unordered_pair2,axiom,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ) ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(cartesian_product1,axiom,
( member(X0,X2)
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ) ).
cnf(cartesian_product2,axiom,
( member(X1,X3)
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ) ).
cnf(cartesian_product3,axiom,
( member('ordered$upair'(X0,X2),'cross$uproduct'(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ) ).
cnf(cartesian_product4,axiom,
( 'ordered$upair'(first(X0),second(X0)) = X0
| ~ member(X0,'cross$uproduct'(X1,X2)) ) ).
cnf(c0,plain,
member('ordered$upair'(u,v),'cross$uproduct'('universal$uclass','universal$uclass')),
inference(clausification,[status(esa)],[prove_unique_1st_and_2nd_in_pair_of_sets2_1]) ).
cnf(c1,plain,
second('ordered$upair'(u,v)) != v,
inference(clausification,[status(esa)],[prove_unique_1st_and_2nd_in_pair_of_sets2_2]) ).
cnf(c9,plain,
( X2 = X1
| ~ member(X1,'unordered$upair'(X0,X2))
| X0 = X1 ),
inference(clausification,[status(esa)],[unordered_pair_member]) ).
cnf(c10,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[unordered_pair2]) ).
cnf(c13,plain,
singleton(X0) = 'unordered$upair'(X0,X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c15,plain,
( member(X0,X2)
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[cartesian_product1]) ).
cnf(c16,plain,
( member(X1,X3)
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[cartesian_product2]) ).
cnf(c17,plain,
( member('ordered$upair'(X2,X0),'cross$uproduct'(X3,X1))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[cartesian_product3]) ).
cnf(c18,plain,
( 'ordered$upair'(first(X0),second(X0)) = X0
| ~ member(X0,'cross$uproduct'(X1,X2)) ),
inference(clausification,[status(esa)],[cartesian_product4]) ).
cnf(d0,plain,
( X0 = X1
| X0 = X1
| ~ member(X1,singleton(X0)) ),
inference(superposition,[status(thm)],[c13,c9]) ).
cnf(d1,plain,
'ordered$upair'(first('ordered$upair'(u,v)),second('ordered$upair'(u,v))) = 'ordered$upair'(u,v),
inference(resolution,[status(thm)],[c18,c0]) ).
cnf(d2,plain,
( member(second('ordered$upair'(u,v)),X1)
| ~ member('ordered$upair'(u,v),'cross$uproduct'(X0,X1)) ),
inference(superposition,[status(thm)],[d1,c16]) ).
cnf(d3,plain,
member(u,'universal$uclass'),
inference(resolution,[status(thm)],[c15,c0]) ).
cnf(d4,plain,
member(v,'universal$uclass'),
inference(resolution,[status(thm)],[c16,c0]) ).
cnf(d5,plain,
member(v,'unordered$upair'(v,X0)),
inference(resolution,[status(thm)],[d4,c10]) ).
cnf(d6,plain,
member(v,singleton(v)),
inference(superposition,[status(thm)],[c13,d5]) ).
cnf(d7,plain,
( member('ordered$upair'(X0,v),'cross$uproduct'(X1,singleton(v)))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[d6,c17]) ).
cnf(d8,plain,
member('ordered$upair'(u,v),'cross$uproduct'('universal$uclass',singleton(v))),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
member(second('ordered$upair'(u,v)),singleton(v)),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
v = second('ordered$upair'(u,v)),
inference(resolution,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
v != v,
inference(demodulation,[status(thm)],[c1,d10]) ).
cnf(d12,plain,
$false,
inference(equality_resolution,[status(thm)],[d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET021-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.47 % Computer : n019.cluster.edu
% 0.09/0.47 % Model : x86_64 x86_64
% 0.09/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.47 % Memory : 8046.5625MB
% 0.09/0.47 % OS : Linux 6.8.0-71-generic
% 0.09/0.47 % CPULimit : 300
% 0.09/0.47 % WCLimit : 300
% 0.09/0.47 % DateTime : Sat Sep 26 06:53:03 UTC 2026
% 0.09/0.47 % CPUTime :
% 0.09/0.47 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 72.04/42.37 % SZS status Unsatisfiable for theBenchmark.p
% 72.04/42.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------