%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET090-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 08:31:59 AM UTC 2026
% Result : Unsatisfiable 34.23s 5.42s
% Output : CNFRefutation 34.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 12 unt; 0 nHn; 21 RR)
% Number of literals : 37 ( 12 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(corollary_1_to_unordered_pair,axiom,
( member(X0,'unordered$upair'(X0,X1))
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ) ).
cnf(only_member_in_singleton,axiom,
( X0 = X1
| ~ member(X0,singleton(X1)) ) ).
cnf(member_exists2,axiom,
( singleton('member$uof'(singleton(X0))) = singleton(X0)
| ~ member(X0,'universal$uclass') ) ).
cnf(prove_member_of_singleton_is_unique_1,negated_conjecture,
member(u,'universal$uclass') ).
cnf(prove_member_of_singleton_is_unique_2,negated_conjecture,
'member$uof'(singleton(u)) != u ).
cnf(singleton_set,axiom,
'unordered$upair'(X0,X0) = singleton(X0) ).
cnf(cartesian_product3,axiom,
( member('ordered$upair'(X0,X2),'cross$uproduct'(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ) ).
cnf(c0,plain,
( member(X0,'unordered$upair'(X0,X1))
| ~ member('ordered$upair'(X0,X1),'cross$uproduct'(X2,X3)) ),
inference(clausification,[status(esa)],[corollary_1_to_unordered_pair]) ).
cnf(c33,plain,
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(clausification,[status(esa)],[only_member_in_singleton]) ).
cnf(c39,plain,
( singleton('member$uof'(singleton(X0))) = singleton(X0)
| ~ member(X0,'universal$uclass') ),
inference(clausification,[status(esa)],[member_exists2]) ).
cnf(c42,plain,
member(u,'universal$uclass'),
inference(clausification,[status(esa)],[prove_member_of_singleton_is_unique_1]) ).
cnf(c43,plain,
'member$uof'(singleton(u)) != u,
inference(clausification,[status(esa)],[prove_member_of_singleton_is_unique_2]) ).
cnf(c55,plain,
'unordered$upair'(X0,X0) = singleton(X0),
inference(clausification,[status(esa)],[singleton_set]) ).
cnf(c59,plain,
( member('ordered$upair'(X0,X2),'cross$uproduct'(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[cartesian_product3]) ).
cnf(d0,plain,
singleton('member$uof'(singleton(u))) = singleton(u),
inference(resolution,[status(thm)],[c39,c42]) ).
cnf(d1,plain,
( X0 = 'member$uof'(singleton(u))
| ~ member(X0,singleton(u)) ),
inference(superposition,[status(thm)],[d0,c33]) ).
cnf(d2,plain,
( member(X2,'unordered$upair'(X2,X0))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[c59,c0]) ).
cnf(d3,plain,
( member(X0,'unordered$upair'(X0,u))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[d2,c42]) ).
cnf(d4,plain,
member(u,'unordered$upair'(u,u)),
inference(resolution,[status(thm)],[d3,c42]) ).
cnf(d5,plain,
member(u,singleton(u)),
inference(demodulation,[status(thm)],[d4,c55]) ).
cnf(d6,plain,
u = 'member$uof'(singleton(u)),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
u != u,
inference(demodulation,[status(thm)],[c43,d6]) ).
cnf(d8,plain,
$false,
inference(equality_resolution,[status(thm)],[d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET090-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n020.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 07:06:04 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.23/5.42 % SZS status Unsatisfiable for theBenchmark.p
% 34.23/5.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------