%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET014-2 : 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 : 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 08:31:34 AM UTC 2026
% Result : Unsatisfiable 31.09s 7.85s
% Output : CNFRefutation 31.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 13 unt; 9 nHn; 26 RR)
% Number of literals : 55 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_subset_of_c,hypothesis,
subset(as,cs) ).
cnf(b_subset_of_c,hypothesis,
subset(bs,cs) ).
cnf(prove_a_union_b_subset_of_c,negated_conjecture,
~ subset(union(as,bs),cs) ).
cnf(membership_in_subsets,axiom,
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ) ).
cnf(subsets_axiom1,axiom,
( member('member$uof$u1$unot$uof$u2'(X0,X1),X0)
| subset(X0,X1) ) ).
cnf(subsets_axiom2,axiom,
( subset(X0,X1)
| ~ member('member$uof$u1$unot$uof$u2'(X0,X1),X1) ) ).
cnf(member_of_set_or_complement,axiom,
( member(X0,complement(X1))
| member(X0,X1) ) ).
cnf(not_member_of_set_and_complement,axiom,
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ) ).
cnf(member_of_union_is_member_of_one_set,axiom,
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ).
cnf(c0,plain,
subset(as,cs),
inference(clausification,[status(esa)],[a_subset_of_c]) ).
cnf(c1,plain,
subset(bs,cs),
inference(clausification,[status(esa)],[b_subset_of_c]) ).
cnf(c2,plain,
~ subset(union(as,bs),cs),
inference(clausification,[status(esa)],[prove_a_union_b_subset_of_c]) ).
cnf(c4,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[membership_in_subsets]) ).
cnf(c5,plain,
( member('member$uof$u1$unot$uof$u2'(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subsets_axiom1]) ).
cnf(c6,plain,
( subset(X0,X1)
| ~ member('member$uof$u1$unot$uof$u2'(X0,X1),X1) ),
inference(clausification,[status(esa)],[subsets_axiom2]) ).
cnf(c7,plain,
( member(X0,complement(X1))
| member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_set_or_complement]) ).
cnf(c8,plain,
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[not_member_of_set_and_complement]) ).
cnf(c11,plain,
( member(X0,X2)
| ~ member(X0,union(X1,X2))
| member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_union_is_member_of_one_set]) ).
cnf(d0,plain,
( ~ member(X0,bs)
| member(X0,cs) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d1,plain,
member('member$uof$u1$unot$uof$u2'(union(as,bs),cs),union(as,bs)),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d2,plain,
( member('member$uof$u1$unot$uof$u2'(union(as,bs),cs),as)
| member('member$uof$u1$unot$uof$u2'(union(as,bs),cs),bs) ),
inference(resolution,[status(thm)],[d1,c11]) ).
cnf(d3,plain,
( ~ member('member$uof$u1$unot$uof$u2'(union(as,bs),cs),complement(as))
| member('member$uof$u1$unot$uof$u2'(union(as,bs),cs),bs) ),
inference(resolution,[status(thm)],[d2,c8]) ).
cnf(d4,plain,
( subset(X0,X1)
| member('member$uof$u1$unot$uof$u2'(X0,X1),complement(X1)) ),
inference(resolution,[status(thm)],[c7,c6]) ).
cnf(d5,plain,
member('member$uof$u1$unot$uof$u2'(union(as,bs),cs),complement(cs)),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
( ~ member(X0,as)
| member(X0,cs) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d7,plain,
( member(X0,complement(as))
| member(X0,cs) ),
inference(resolution,[status(thm)],[d6,c7]) ).
cnf(d8,plain,
( ~ member(X0,complement(cs))
| member(X0,complement(as)) ),
inference(resolution,[status(thm)],[d7,c8]) ).
cnf(d9,plain,
member('member$uof$u1$unot$uof$u2'(union(as,bs),cs),complement(as)),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
member('member$uof$u1$unot$uof$u2'(union(as,bs),cs),bs),
inference(resolution,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
member('member$uof$u1$unot$uof$u2'(union(as,bs),cs),cs),
inference(resolution,[status(thm)],[d10,d0]) ).
cnf(d12,plain,
subset(union(as,bs),cs),
inference(resolution,[status(thm)],[d11,c6]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[c2,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET014-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.43 % Computer : n001.cluster.edu
% 0.08/0.43 % Model : x86_64 x86_64
% 0.08/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.43 % Memory : 8046.5625MB
% 0.08/0.43 % OS : Linux 6.8.0-71-generic
% 0.08/0.43 % CPULimit : 300
% 0.08/0.43 % WCLimit : 300
% 0.08/0.43 % DateTime : Sat Sep 26 06:55:43 UTC 2026
% 0.08/0.43 % CPUTime :
% 0.08/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.09/7.85 % SZS status Unsatisfiable for theBenchmark.p
% 31.09/7.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------