%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET347-6 : 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 : n003.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 08:32:30 AM UTC 2026
% Result : Unsatisfiable 110.87s 36.34s
% Output : CNFRefutation 110.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of clauses : 61 ( 26 unt; 13 nHn; 35 RR)
% Number of literals : 106 ( 38 equ; 40 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 : 15 ( 15 usr; 3 con; 0-3 aty)
% Number of variables : 105 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_sum_class_of_null_class_1,negated_conjecture,
'sum$uclass'('null$uclass') != 'null$uclass' ).
cnf(subclass_members,axiom,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ) ).
cnf(not_subclass_members1,axiom,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ) ).
cnf(not_subclass_members2,axiom,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ) ).
cnf(class_elements_are_sets,axiom,
subclass(X0,'universal$uclass') ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(cartesian_product2,axiom,
( member(X1,X3)
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ) ).
cnf(cartesian_product4,axiom,
( 'ordered$upair'(first(X0),second(X0)) = X0
| ~ member(X0,'cross$uproduct'(X1,X2)) ) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(restriction1,axiom,
intersection(X0,'cross$uproduct'(X1,X2)) = restrict(X0,X1,X2) ).
cnf(restriction2,axiom,
intersection('cross$uproduct'(X0,X1),X2) = restrict(X2,X0,X1) ).
cnf(domain1,axiom,
( ~ member(X1,'domain$uof'(X0))
| restrict(X0,singleton(X1),'universal$uclass') != 'null$uclass' ) ).
cnf(sum_class_definition,axiom,
'domain$uof'(restrict('element$urelation','universal$uclass',X0)) = 'sum$uclass'(X0) ).
cnf(regularity1,axiom,
( member(regular(X0),X0)
| X0 = 'null$uclass' ) ).
cnf(c0,plain,
'sum$uclass'('null$uclass') != 'null$uclass',
inference(clausification,[status(esa)],[prove_sum_class_of_null_class_1]) ).
cnf(c1,plain,
( member(X0,X2)
| ~ subclass(X1,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[subclass_members]) ).
cnf(c2,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c3,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c4,plain,
subclass(X0,'universal$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c7,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c15,plain,
( member(X1,X3)
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[cartesian_product2]) ).
cnf(c17,plain,
( 'ordered$upair'(first(X0),second(X0)) = X0
| ~ member(X0,'cross$uproduct'(X1,X2)) ),
inference(clausification,[status(esa)],[cartesian_product4]) ).
cnf(c21,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c24,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c28,plain,
restrict(X0,X1,X2) = intersection(X0,'cross$uproduct'(X1,X2)),
inference(clausification,[status(esa)],[restriction1]) ).
cnf(c29,plain,
restrict(X0,X1,X2) = intersection('cross$uproduct'(X1,X2),X0),
inference(clausification,[status(esa)],[restriction2]) ).
cnf(c30,plain,
( ~ member(X1,'domain$uof'(X0))
| restrict(X0,singleton(X1),'universal$uclass') != 'null$uclass' ),
inference(clausification,[status(esa)],[domain1]) ).
cnf(c53,plain,
'sum$uclass'(X0) = 'domain$uof'(restrict('element$urelation','universal$uclass',X0)),
inference(clausification,[status(esa)],[sum_class_definition]) ).
cnf(c66,plain,
( member(regular(X0),X0)
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(d0,plain,
( complement(X0) = 'null$uclass'
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[c24,c66]) ).
cnf(d1,plain,
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[c66,c1]) ).
cnf(d2,plain,
( complement(X0) = 'null$uclass'
| ~ subclass(complement(X0),X0)
| complement(X0) = 'null$uclass' ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
complement('universal$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
( member('not$usubclass$uelement'(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[c2,c1]) ).
cnf(d5,plain,
( subclass(complement(X0),X1)
| ~ member('not$usubclass$uelement'(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[c24,c2]) ).
cnf(d6,plain,
( subclass(complement(X0),X1)
| ~ subclass(complement(X0),X0)
| subclass(complement(X0),X1) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
subclass(complement('universal$uclass'),X0),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
subclass('null$uclass',X0),
inference(demodulation,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
( ~ subclass(X0,'null$uclass')
| 'null$uclass' = X0 ),
inference(resolution,[status(thm)],[d8,c7]) ).
cnf(d10,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c21,c2]) ).
cnf(d11,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d10,c3]) ).
cnf(d12,plain,
'null$uclass' = intersection('null$uclass',X0),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
restrict('null$uclass',X0,X1) = 'null$uclass',
inference(superposition,[status(thm)],[d12,c28]) ).
cnf(d14,plain,
( ~ member(X0,'domain$uof'('null$uclass'))
| 'null$uclass' != 'null$uclass' ),
inference(superposition,[status(thm)],[d13,c30]) ).
cnf(d15,plain,
( complement('universal$uclass') = 'null$uclass'
| ~ subclass('null$uclass','universal$uclass') ),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d16,plain,
( ~ subclass('null$uclass','universal$uclass')
| 'null$uclass' = 'null$uclass' ),
inference(demodulation,[status(thm)],[d15,d3]) ).
cnf(d17,plain,
'null$uclass' = 'null$uclass',
inference(resolution,[status(thm)],[c4,d16]) ).
cnf(d18,plain,
~ member(X0,'domain$uof'('null$uclass')),
inference(resolution,[status(thm)],[d17,d14]) ).
cnf(d19,plain,
'domain$uof'('null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d18,c66]) ).
cnf(d20,plain,
subclass(restrict(X2,X0,X1),'cross$uproduct'(X0,X1)),
inference(superposition,[status(thm)],[c29,d11]) ).
cnf(d21,plain,
~ member(X0,'null$uclass'),
inference(demodulation,[status(thm)],[d18,d19]) ).
cnf(d22,plain,
( 'cross$uproduct'(X0,X1) = 'null$uclass'
| 'ordered$upair'(first(regular('cross$uproduct'(X0,X1))),second(regular('cross$uproduct'(X0,X1)))) = regular('cross$uproduct'(X0,X1)) ),
inference(resolution,[status(thm)],[c17,c66]) ).
cnf(d23,plain,
( 'cross$uproduct'(X0,X1) = 'null$uclass'
| member(second(regular('cross$uproduct'(X0,X1))),X3)
| ~ member(regular('cross$uproduct'(X0,X1)),'cross$uproduct'(X2,X3)) ),
inference(superposition,[status(thm)],[d22,c15]) ).
cnf(d24,plain,
( 'cross$uproduct'(X0,X1) = 'null$uclass'
| member(second(regular('cross$uproduct'(X0,X1))),X1)
| 'cross$uproduct'(X0,X1) = 'null$uclass' ),
inference(resolution,[status(thm)],[d23,c66]) ).
cnf(d25,plain,
'cross$uproduct'(X0,'null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
subclass(restrict(X1,X0,'null$uclass'),'null$uclass'),
inference(superposition,[status(thm)],[d25,d20]) ).
cnf(d27,plain,
'null$uclass' = restrict(X0,X1,'null$uclass'),
inference(resolution,[status(thm)],[d26,d9]) ).
cnf(d28,plain,
'sum$uclass'('null$uclass') = 'domain$uof'('null$uclass'),
inference(superposition,[status(thm)],[d27,c53]) ).
cnf(d29,plain,
'sum$uclass'('null$uclass') = 'null$uclass',
inference(demodulation,[status(thm)],[d28,d19]) ).
cnf(d30,plain,
$false,
inference(resolution,[status(thm)],[c0,d29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET347-6 : 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 : n003.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 07:35:24 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 110.87/36.34 % SZS status Unsatisfiable for theBenchmark.p
% 110.87/36.34 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------