%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET231-6 : 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 : n013.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 19.11s 3.16s
% Output : CNFRefutation 19.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 6 unt; 3 nHn; 8 RR)
% Number of literals : 16 ( 6 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 : 13 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_cross_product_property6_1,negated_conjecture,
~ subclass('cross$uproduct'(x,y),z) ).
cnf(prove_cross_product_property6_2,negated_conjecture,
'ordered$upair'(first('not$usubclass$uelement'('cross$uproduct'(x,y),z)),second('not$usubclass$uelement'('cross$uproduct'(x,y),z))) != 'not$usubclass$uelement'('cross$uproduct'(x,y),z) ).
cnf(not_subclass_members1,axiom,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ) ).
cnf(cartesian_product4,axiom,
( 'ordered$upair'(first(X0),second(X0)) = X0
| ~ member(X0,'cross$uproduct'(X1,X2)) ) ).
cnf(c0,plain,
~ subclass('cross$uproduct'(x,y),z),
inference(clausification,[status(esa)],[prove_cross_product_property6_1]) ).
cnf(c1,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(clausification,[status(esa)],[prove_cross_product_property6_2]) ).
cnf(c3,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
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,c0]) ).
cnf(d2,plain,
$false,
inference(resolution,[status(thm)],[c1,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET231-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.58 % Computer : n013.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Sat Sep 26 07:22:27 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.11/3.16 % SZS status Unsatisfiable for theBenchmark.p
% 19.11/3.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------