%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET204-6 : 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 : n012.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 08:32:19 AM UTC 2026
% Result : Unsatisfiable 14.85s 2.22s
% Output : CNFRefutation 14.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 8 unt; 0 nHn; 15 RR)
% Number of literals : 24 ( 0 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 24 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_cross_product_property2_1,negated_conjecture,
member('ordered$upair'(u,v),'cross$uproduct'(x,y)) ).
cnf(prove_cross_product_property2_2,negated_conjecture,
~ member('ordered$upair'(v,u),'cross$uproduct'(y,x)) ).
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(c0,plain,
member('ordered$upair'(u,v),'cross$uproduct'(x,y)),
inference(clausification,[status(esa)],[prove_cross_product_property2_1]) ).
cnf(c1,plain,
~ member('ordered$upair'(v,u),'cross$uproduct'(y,x)),
inference(clausification,[status(esa)],[prove_cross_product_property2_2]) ).
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$upair'(X0,X2),'cross$uproduct'(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[cartesian_product3]) ).
cnf(d0,plain,
( ~ member(v,y)
| ~ member(u,x) ),
inference(resolution,[status(thm)],[c17,c1]) ).
cnf(d1,plain,
member(u,x),
inference(resolution,[status(thm)],[c15,c0]) ).
cnf(d2,plain,
~ member(v,y),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
member(v,y),
inference(resolution,[status(thm)],[c16,c0]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[d3,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET204-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sat Sep 26 07:19:21 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.85/2.22 % SZS status Unsatisfiable for theBenchmark.p
% 14.85/2.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------