%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET411-6 : 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 : n002.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 08:32:35 AM UTC 2026
% Result : Unsatisfiable 14.01s 2.75s
% Output : CNFRefutation 14.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 12 unt; 0 nHn; 18 RR)
% Number of literals : 30 ( 2 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 21 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_compose_condition_for_singleton_membership1_1,negated_conjecture,
member('ordered$upair'(x,y),'singleton$urelation') ).
cnf(prove_compose_condition_for_singleton_membership1_2,negated_conjecture,
~ member(x,'universal$uclass') ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(class_elements_are_sets,axiom,
subclass(X0,'universal$uclass') ).
cnf(element_relation2,axiom,
( member(X0,X1)
| ~ member('ordered$upair'(X0,X1),'element$urelation') ) ).
cnf(intersection2,axiom,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(compose_can_define_singleton,axiom,
intersection(complement(compose('element$urelation',complement('identity$urelation'))),'element$urelation') = 'singleton$urelation' ).
cnf(c0,plain,
member('ordered$upair'(x,y),'singleton$urelation'),
inference(clausification,[status(esa)],[prove_compose_condition_for_singleton_membership1_1]) ).
cnf(c1,plain,
~ member(x,'universal$uclass'),
inference(clausification,[status(esa)],[prove_compose_condition_for_singleton_membership1_2]) ).
cnf(c2,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c5,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c20,plain,
( member(X0,X1)
| ~ member('ordered$upair'(X0,X1),'element$urelation') ),
inference(clausification,[status(esa)],[element_relation2]) ).
cnf(c23,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c105,plain,
intersection(complement(compose('element$urelation',complement('identity$urelation'))),'element$urelation') = 'singleton$urelation',
inference(clausification,[status(esa)],[compose_can_define_singleton]) ).
cnf(d0,plain,
( ~ member(X0,X1)
| member(X0,'universal$uclass') ),
inference(resolution,[status(thm)],[c2,c5]) ).
cnf(d1,plain,
( member(X0,'element$urelation')
| ~ member(X0,'singleton$urelation') ),
inference(superposition,[status(thm)],[c105,c23]) ).
cnf(d2,plain,
member('ordered$upair'(x,y),'element$urelation'),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
member(x,y),
inference(resolution,[status(thm)],[d2,c20]) ).
cnf(d4,plain,
member(x,'universal$uclass'),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c1,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET411-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n002.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 26 07:43:05 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.01/2.75 % SZS status Unsatisfiable for theBenchmark.p
% 14.01/2.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------