%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 08:31:31 AM UTC 2026
% Result : Unsatisfiable 10.35s 2.00s
% Output : CNFRefutation 10.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 5 unt; 4 nHn; 11 RR)
% Number of literals : 25 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_union_b_is_aUb,hypothesis,
union(a,b,aUb) ).
cnf(prove_a_is_a_subset_of_aUb,negated_conjecture,
~ subset(a,aUb) ).
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_set1_is_member_of_union,axiom,
( member(X3,X2)
| ~ member(X3,X0)
| ~ union(X0,X1,X2) ) ).
cnf(c0,plain,
union(a,b,aUb),
inference(clausification,[status(esa)],[a_union_b_is_aUb]) ).
cnf(c1,plain,
~ subset(a,aUb),
inference(clausification,[status(esa)],[prove_a_is_a_subset_of_aUb]) ).
cnf(c3,plain,
( member('member$uof$u1$unot$uof$u2'(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subsets_axiom1]) ).
cnf(c4,plain,
( subset(X0,X1)
| ~ member('member$uof$u1$unot$uof$u2'(X0,X1),X1) ),
inference(clausification,[status(esa)],[subsets_axiom2]) ).
cnf(c9,plain,
( member(X3,X2)
| ~ member(X3,X0)
| ~ union(X0,X1,X2) ),
inference(clausification,[status(esa)],[member_of_set1_is_member_of_union]) ).
cnf(d0,plain,
( ~ member(X0,a)
| member(X0,aUb) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d1,plain,
( subset(a,X0)
| member('member$uof$u1$unot$uof$u2'(a,X0),aUb) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( subset(a,aUb)
| subset(a,aUb) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c1,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.57 % Computer : n014.cluster.edu
% 0.11/0.57 % Model : x86_64 x86_64
% 0.11/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.57 % Memory : 8046.5625MB
% 0.11/0.57 % OS : Linux 6.8.0-71-generic
% 0.11/0.57 % CPULimit : 300
% 0.11/0.57 % WCLimit : 300
% 0.11/0.57 % DateTime : Sat Sep 26 06:47:47 UTC 2026
% 0.11/0.58 % CPUTime :
% 0.11/0.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.35/2.00 % SZS status Unsatisfiable for theBenchmark.p
% 10.35/2.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------