%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM190-1 : 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 : n001.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 08:10:52 AM UTC 2026
% Result : Unsatisfiable 13.37s 13.04s
% Output : CNFRefutation 13.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 33 ( 9 unt; 10 nHn; 21 RR)
% Number of literals : 60 ( 12 equ; 20 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_omega_is_not_null_1,negated_conjecture,
omega = 'null$uclass' ).
cnf(not_subclass_members1,axiom,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ) ).
cnf(not_subclass_members2,axiom,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ) ).
cnf(subclass_implies_equal,axiom,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection2,axiom,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(inductive1,axiom,
( member('null$uclass',X0)
| ~ inductive(X0) ) ).
cnf(omega_is_inductive1,axiom,
inductive(omega) ).
cnf(regularity2,axiom,
( intersection(X0,regular(X0)) = 'null$uclass'
| X0 = 'null$uclass' ) ).
cnf(c0,plain,
omega = 'null$uclass',
inference(clausification,[status(esa)],[prove_omega_is_not_null_1]) ).
cnf(c2,plain,
( subclass(X0,X1)
| member('not$usubclass$uelement'(X0,X1),X0) ),
inference(clausification,[status(esa)],[not_subclass_members1]) ).
cnf(c3,plain,
( subclass(X0,X1)
| ~ member('not$usubclass$uelement'(X0,X1),X1) ),
inference(clausification,[status(esa)],[not_subclass_members2]) ).
cnf(c7,plain,
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(clausification,[status(esa)],[subclass_implies_equal]) ).
cnf(c21,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c22,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c24,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c47,plain,
( member('null$uclass',X0)
| ~ inductive(X0) ),
inference(clausification,[status(esa)],[inductive1]) ).
cnf(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,
( ~ inductive(intersection(X0,X1))
| member('null$uclass',X0) ),
inference(resolution,[status(thm)],[c21,c47]) ).
cnf(d1,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c22,c2]) ).
cnf(d2,plain,
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( subclass(intersection(X0,X1),X2)
| member('not$usubclass$uelement'(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[c21,c2]) ).
cnf(d4,plain,
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
( X0 = 'null$uclass'
| subclass('null$uclass',X0) ),
inference(superposition,[status(thm)],[c67,d4]) ).
cnf(d6,plain,
( ~ subclass(X0,'null$uclass')
| X0 = 'null$uclass'
| X0 = 'null$uclass' ),
inference(resolution,[status(thm)],[d5,c7]) ).
cnf(d7,plain,
intersection(X0,'null$uclass') = 'null$uclass',
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( member('null$uclass',X0)
| ~ inductive('null$uclass') ),
inference(superposition,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
inductive('null$uclass'),
inference(demodulation,[status(thm)],[c50,c0]) ).
cnf(d10,plain,
member('null$uclass',X0),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
~ member('null$uclass',X0),
inference(resolution,[status(thm)],[d10,c24]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d10,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM190-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.38 % Computer : n001.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Sat Sep 26 02:17:08 UTC 2026
% 0.11/10.38 % CPUTime :
% 0.11/10.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.37/13.04 % SZS status Unsatisfiable for theBenchmark.p
% 13.37/13.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------