%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET234-6 : 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 08:32:21 AM UTC 2026
% Result : Unsatisfiable 15.51s 4.32s
% Output : CNFRefutation 15.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 15 ( 8 unt; 3 nHn; 12 RR)
% Number of literals : 22 ( 4 equ; 6 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 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 : 17 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_cross_product_property9_1,negated_conjecture,
member('ordered$upair'(first('not$usubclass$uelement'('cross$uproduct'(x,y),z)),second('not$usubclass$uelement'('cross$uproduct'(x,y),z))),z) ).
cnf(prove_cross_product_property9_2,negated_conjecture,
~ subclass('cross$uproduct'(x,y),z) ).
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,
member('ordered$upair'(first('not$usubclass$uelement'('cross$uproduct'(x,y),z)),second('not$usubclass$uelement'('cross$uproduct'(x,y),z))),z),
inference(clausification,[status(esa)],[prove_cross_product_property9_1]) ).
cnf(c1,plain,
~ subclass('cross$uproduct'(x,y),z),
inference(clausification,[status(esa)],[prove_cross_product_property9_2]) ).
cnf(c3,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c4,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
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,
( subclass('cross$uproduct'(X0,X1),X2)
| 'ordered$upair'(first('not$usubclass$uelement'('cross$uproduct'(X0,X1),X2)),second('not$usubclass$uelement'('cross$uproduct'(X0,X1),X2))) = 'not$usubclass$uelement'('cross$uproduct'(X0,X1),X2) ),
inference(resolution,[status(thm)],[c18,c3]) ).
cnf(d1,plain,
'ordered$upair'(first('not$usubclass$uelement'('cross$uproduct'(x,y),z)),second('not$usubclass$uelement'('cross$uproduct'(x,y),z))) = 'not$usubclass$uelement'('cross$uproduct'(x,y),z),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
member('not$usubclass$uelement'('cross$uproduct'(x,y),z),z),
inference(demodulation,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
subclass('cross$uproduct'(x,y),z),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[c1,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET234-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n019.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 07:22:52 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.51/4.32 % SZS status Unsatisfiable for theBenchmark.p
% 15.51/4.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------