%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET230-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 40.53s 5.59s
% Output : CNFRefutation 40.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 30 ( 7 unt; 6 nHn; 26 RR)
% Number of literals : 60 ( 9 equ; 27 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_corollary_to_cross_product_cancellation_1,negated_conjecture,
'cross$uproduct'(u,u) = 'cross$uproduct'(w,w) ).
cnf(prove_corollary_to_cross_product_cancellation_2,negated_conjecture,
u != w ).
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(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
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,
'cross$uproduct'(u,u) = 'cross$uproduct'(w,w),
inference(clausification,[status(esa)],[prove_corollary_to_cross_product_cancellation_1]) ).
cnf(c1,plain,
u != w,
inference(clausification,[status(esa)],[prove_corollary_to_cross_product_cancellation_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(c8,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
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(X0,w)
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(u,u)) ),
inference(superposition,[status(thm)],[c0,c15]) ).
cnf(d1,plain,
( ~ member(X0,u)
| ~ member(X1,u)
| member(X0,w) ),
inference(resolution,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
( member(X0,w)
| ~ member(X0,u) ),
inference(factoring,[status(thm)],[d1]) ).
cnf(d3,plain,
( subclass(u,X0)
| member('not$usubclass$uelement'(u,X0),w) ),
inference(resolution,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
( subclass(u,w)
| subclass(u,w) ),
inference(resolution,[status(thm)],[d3,c4]) ).
cnf(d5,plain,
( ~ subclass(w,u)
| w = u ),
inference(resolution,[status(thm)],[d4,c8]) ).
cnf(d6,plain,
( ~ member(X0,w)
| ~ member(X1,w)
| member('ordered$upair'(X0,X1),'cross$uproduct'(u,u)) ),
inference(superposition,[status(thm)],[c0,c17]) ).
cnf(d7,plain,
( member(X0,u)
| ~ member(X1,w)
| ~ member(X0,w) ),
inference(resolution,[status(thm)],[d6,c16]) ).
cnf(d8,plain,
( member(X0,u)
| ~ member(X0,w) ),
inference(factoring,[status(thm)],[d7]) ).
cnf(d9,plain,
( subclass(w,X0)
| member('not$usubclass$uelement'(w,X0),u) ),
inference(resolution,[status(thm)],[d8,c3]) ).
cnf(d10,plain,
( subclass(w,u)
| subclass(w,u) ),
inference(resolution,[status(thm)],[d9,c4]) ).
cnf(d11,plain,
w = u,
inference(resolution,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
u != u,
inference(demodulation,[status(thm)],[c1,d11]) ).
cnf(d13,plain,
$false,
inference(equality_resolution,[status(thm)],[d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET230-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n005.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 07:22:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 40.53/5.59 % SZS status Unsatisfiable for theBenchmark.p
% 40.53/5.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------