%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET507-6 : 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 : n006.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 08:32:42 AM UTC 2026
% Result : Unsatisfiable 18.84s 4.08s
% Output : CNFRefutation 18.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 46 ( 14 unt; 10 nHn; 32 RR)
% Number of literals : 88 ( 16 equ; 37 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_universal_class_not_subclass_of_null_class_1,negated_conjecture,
subclass('universal$uclass','null$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$uclass') ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(inductive1,axiom,
( member('null$uclass',X0)
| ~ inductive(X0) ) ).
cnf(inductive3,axiom,
( inductive(X0)
| ~ subclass(image('successor$urelation',X0),X0)
| ~ member('null$uclass',X0) ) ).
cnf(omega_is_inductive1,axiom,
inductive(omega) ).
cnf(regularity2,axiom,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ) ).
cnf(c0,plain,
subclass('universal$uclass','null$uclass'),
inference(clausification,[status(esa)],[prove_universal_class_not_subclass_of_null_class_1]) ).
cnf(c1,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(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$uclass'),
inference(clausification,[status(esa)],[class_elements_are_sets]) ).
cnf(c7,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c21,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c24,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c47,plain,
( member('null$uclass',X0)
| ~ inductive(X0) ),
inference(clausification,[status(esa)],[inductive1]) ).
cnf(c49,plain,
( inductive(X0)
| ~ subclass(image('successor$urelation',X0),X0)
| ~ member('null$uclass',X0) ),
inference(clausification,[status(esa)],[inductive3]) ).
cnf(c50,plain,
inductive(omega),
inference(clausification,[status(esa)],[omega_is_inductive1]) ).
cnf(c67,plain,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ),
inference(clausification,[status(esa)],[regularity2]) ).
cnf(d0,plain,
( ~ subclass('universal$uclass',X0)
| 'universal$uclass' = X0 ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(d1,plain,
'universal$uclass' = 'null$uclass',
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
( ~ inductive(complement(X0))
| ~ member('null$uclass',X0) ),
inference(resolution,[status(thm)],[c24,c47]) ).
cnf(d3,plain,
( ~ inductive(complement(X0))
| ~ member('universal$uclass',X0) ),
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( inductive(X0)
| ~ member('universal$uclass',X0)
| ~ subclass(image('successor$urelation',X0),X0) ),
inference(demodulation,[status(thm)],[c49,d1]) ).
cnf(d5,plain,
( inductive('universal$uclass')
| ~ member('universal$uclass','universal$uclass') ),
inference(resolution,[status(thm)],[d4,c4]) ).
cnf(d6,plain,
( member('null$uclass',X1)
| ~ subclass(X0,X1)
| ~ inductive(X0) ),
inference(resolution,[status(thm)],[c47,c1]) ).
cnf(d7,plain,
( ~ inductive(X0)
| member('universal$uclass',X1)
| ~ subclass(X0,X1) ),
inference(demodulation,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( ~ inductive(X0)
| member('universal$uclass','universal$uclass') ),
inference(resolution,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
member('universal$uclass','universal$uclass'),
inference(resolution,[status(thm)],[d8,c50]) ).
cnf(d10,plain,
inductive('universal$uclass'),
inference(resolution,[status(thm)],[d9,d5]) ).
cnf(d11,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c21,c2]) ).
cnf(d12,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d11,c3]) ).
cnf(d13,plain,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'universal$uclass' ),
inference(demodulation,[status(thm)],[c67,d1]) ).
cnf(d14,plain,
( intersection(X0,regular(X0)) = 'universal$uclass'
| X0 = 'universal$uclass' ),
inference(demodulation,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
( X0 = 'universal$uclass'
| subclass('universal$uclass',X0) ),
inference(superposition,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
( ~ subclass(X0,'universal$uclass')
| X0 = 'universal$uclass'
| X0 = 'universal$uclass' ),
inference(resolution,[status(thm)],[d15,c7]) ).
cnf(d17,plain,
X0 = 'universal$uclass',
inference(resolution,[status(thm)],[c4,d16]) ).
cnf(d18,plain,
inductive(X0),
inference(superposition,[status(thm)],[d17,d10]) ).
cnf(d19,plain,
~ member('universal$uclass',X0),
inference(resolution,[status(thm)],[d18,d3]) ).
cnf(d20,plain,
member('universal$uclass',X0),
inference(superposition,[status(thm)],[d17,d9]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[d20,d19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET507-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 07:50:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.84/4.08 % SZS status Unsatisfiable for theBenchmark.p
% 18.84/4.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------