%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUM011-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 08:10:38 AM UTC 2026
% Result : Unsatisfiable 2.49s 16.20s
% Output : CNFRefutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 47 ( 17 unt; 11 nHn; 28 RR)
% Number of literals : 90 ( 17 equ; 38 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 67 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_natural_number,hypothesis,
member(f75,'natural$unumbers') ).
cnf(prove_zero_is_first,negated_conjecture,
'empty$uset' = successor(f75) ).
cnf(a2,axiom,
( 'little$uset'(X0)
| ~ member(X0,X1) ) ).
cnf(non_ordered_pair2,axiom,
( X0 != X1
| ~ 'little$uset'(X0)
| member(X0,'non$uordered$upair'(X1,X2)) ) ).
cnf(singleton_set,axiom,
'singleton$uset'(X0) = 'non$uordered$upair'(X0,X0) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection2,axiom,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(complement1,axiom,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ) ).
cnf(complement2,axiom,
( member(X0,X1)
| ~ 'little$uset'(X0)
| member(X0,complement(X1)) ) ).
cnf(union,axiom,
union(X0,X1) = complement(intersection(complement(X0),complement(X1))) ).
cnf(successor,axiom,
successor(X0) = union(X0,'singleton$uset'(X0)) ).
cnf(empty_set,axiom,
~ member(X0,'empty$uset') ).
cnf(regularity1,axiom,
( member(f24(X0),X0)
| X0 = 'empty$uset' ) ).
cnf(c0,plain,
member(f75,'natural$unumbers'),
inference(clausification,[status(esa)],[a_natural_number]) ).
cnf(c1,plain,
successor(f75) = 'empty$uset',
inference(clausification,[status(esa)],[prove_zero_is_first]) ).
cnf(c2,plain,
( 'little$uset'(X0)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[a2]) ).
cnf(c7,plain,
( X1 != X0
| member(X0,'non$uordered$upair'(X1,X2))
| ~ 'little$uset'(X0) ),
inference(clausification,[status(esa)],[non_ordered_pair2]) ).
cnf(c10,plain,
'non$uordered$upair'(X0,X0) = 'singleton$uset'(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c29,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c30,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c32,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(clausification,[status(esa)],[complement1]) ).
cnf(c33,plain,
( member(X0,X1)
| member(X0,complement(X1))
| ~ 'little$uset'(X0) ),
inference(clausification,[status(esa)],[complement2]) ).
cnf(c34,plain,
complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(clausification,[status(esa)],[union]) ).
cnf(c58,plain,
union(X0,'singleton$uset'(X0)) = successor(X0),
inference(clausification,[status(esa)],[successor]) ).
cnf(c59,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set]) ).
cnf(c99,plain,
( member(f24(X0),X0)
| X0 = 'empty$uset' ),
inference(clausification,[status(esa)],[regularity1]) ).
cnf(d0,plain,
( ~ 'little$uset'(X0)
| member(X0,'non$uordered$upair'(X0,X1)) ),
inference(equality_resolution,[status(thm)],[c7]) ).
cnf(d1,plain,
( ~ 'little$uset'(X0)
| member(X0,'singleton$uset'(X0)) ),
inference(superposition,[status(thm)],[c10,d0]) ).
cnf(d2,plain,
( ~ 'little$uset'(X2)
| member(X2,intersection(complement(X0),complement(X1)))
| member(X2,union(X0,X1)) ),
inference(superposition,[status(thm)],[c34,c33]) ).
cnf(d3,plain,
( member(X0,complement(X2))
| ~ 'little$uset'(X0)
| member(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[d2,c30]) ).
cnf(d4,plain,
( ~ 'little$uset'(X1)
| member(X1,complement('singleton$uset'(X0)))
| member(X1,successor(X0)) ),
inference(superposition,[status(thm)],[c58,d3]) ).
cnf(d5,plain,
( ~ member(X0,'singleton$uset'(X1))
| ~ 'little$uset'(X0)
| member(X0,successor(X1)) ),
inference(resolution,[status(thm)],[d4,c32]) ).
cnf(d6,plain,
( ~ 'little$uset'(X0)
| ~ 'little$uset'(X0)
| member(X0,successor(X0)) ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( 'little$uset'(f24(X0))
| X0 = 'empty$uset' ),
inference(resolution,[status(thm)],[c99,c2]) ).
cnf(d8,plain,
( member(X0,complement(X1))
| ~ 'little$uset'(X0)
| member(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[d2,c29]) ).
cnf(d9,plain,
( ~ 'little$uset'(X1)
| member(X1,complement(X0))
| member(X1,successor(X0)) ),
inference(superposition,[status(thm)],[c58,d8]) ).
cnf(d10,plain,
( ~ member(X0,X1)
| ~ 'little$uset'(X0)
| member(X0,successor(X1)) ),
inference(resolution,[status(thm)],[d9,c32]) ).
cnf(d11,plain,
( ~ 'little$uset'(X0)
| ~ member(X0,f75)
| member(X0,'empty$uset') ),
inference(superposition,[status(thm)],[c1,d10]) ).
cnf(d12,plain,
( ~ 'little$uset'(X0)
| ~ member(X0,f75) ),
inference(resolution,[status(thm)],[c59,d11]) ).
cnf(d13,plain,
( f75 = 'empty$uset'
| ~ 'little$uset'(f24(f75)) ),
inference(resolution,[status(thm)],[d12,c99]) ).
cnf(d14,plain,
( f75 = 'empty$uset'
| f75 = 'empty$uset' ),
inference(resolution,[status(thm)],[d13,d7]) ).
cnf(d15,plain,
successor(f75) = f75,
inference(demodulation,[status(thm)],[c1,d14]) ).
cnf(d16,plain,
( ~ 'little$uset'(f75)
| member(f75,f75) ),
inference(superposition,[status(thm)],[d15,d6]) ).
cnf(d17,plain,
'little$uset'(f75),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d18,plain,
member(f75,f75),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
~ member(X0,f75),
inference(demodulation,[status(thm)],[c59,d14]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d19,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM011-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.53 % Computer : n009.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.53 % CPULimit : 300
% 0.10/0.53 % WCLimit : 300
% 0.10/0.53 % DateTime : Sat Sep 26 01:53:00 UTC 2026
% 0.10/0.53 % CPUTime :
% 0.10/0.53 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.49/16.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.49/16.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------