%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET015-1 : 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 : 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 08:31:34 AM UTC 2026
% Result : Unsatisfiable 49.44s 17.47s
% Output : CNFRefutation 49.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 22 ( 4 unt; 7 nHn; 12 RR)
% Number of literals : 46 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_commutativity,negated_conjecture,
~ 'equal$usets'(union(as,bs),union(bs,as)) ).
cnf(subsets_axiom1,axiom,
( member('member$uof$u1$unot$uof$u2'(X0,X1),X0)
| subset(X0,X1) ) ).
cnf(subsets_axiom2,axiom,
( subset(X0,X1)
| ~ member('member$uof$u1$unot$uof$u2'(X0,X1),X1) ) ).
cnf(member_of_set1_is_member_of_union,axiom,
( member(X0,union(X1,X2))
| ~ member(X0,X1) ) ).
cnf(member_of_set2_is_member_of_union,axiom,
( member(X0,union(X2,X1))
| ~ member(X0,X1) ) ).
cnf(member_of_union_is_member_of_one_set,axiom,
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ).
cnf(subsets_are_set_equal_sets,axiom,
( 'equal$usets'(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ).
cnf(c0,plain,
~ 'equal$usets'(union(as,bs),union(bs,as)),
inference(clausification,[status(esa)],[prove_commutativity]) ).
cnf(c3,plain,
( member('member$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$u2'(X0,X1),X1) ),
inference(clausification,[status(esa)],[subsets_axiom2]) ).
cnf(c7,plain,
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_set1_is_member_of_union]) ).
cnf(c8,plain,
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_set2_is_member_of_union]) ).
cnf(c9,plain,
( member(X0,X2)
| ~ member(X0,union(X1,X2))
| member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_union_is_member_of_one_set]) ).
cnf(c15,plain,
( 'equal$usets'(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subsets_are_set_equal_sets]) ).
cnf(d0,plain,
( subset(X0,union(X1,X2))
| ~ member('member$uof$u1$unot$uof$u2'(X0,union(X1,X2)),X2) ),
inference(resolution,[status(thm)],[c8,c4]) ).
cnf(d1,plain,
( subset(X0,union(X1,X2))
| ~ member('member$uof$u1$unot$uof$u2'(X0,union(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(d2,plain,
( subset(union(X0,X1),X2)
| member('member$uof$u1$unot$uof$u2'(union(X0,X1),X2),X0)
| member('member$uof$u1$unot$uof$u2'(union(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c9,c3]) ).
cnf(d3,plain,
( subset(union(X0,X1),union(X1,X2))
| subset(union(X0,X1),union(X1,X2))
| member('member$uof$u1$unot$uof$u2'(union(X0,X1),union(X1,X2)),X0) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
( subset(union(X0,X1),union(X1,X0))
| subset(union(X0,X1),union(X1,X0)) ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ subset(union(X1,X0),union(X0,X1))
| 'equal$usets'(union(X0,X1),union(X1,X0)) ),
inference(resolution,[status(thm)],[d4,c15]) ).
cnf(d6,plain,
'equal$usets'(union(X0,X1),union(X1,X0)),
inference(resolution,[status(thm)],[d4,d5]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET015-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.39 % Computer : n014.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Sat Sep 26 06:50:38 UTC 2026
% 0.17/5.40 % CPUTime :
% 0.17/5.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.44/17.47 % SZS status Unsatisfiable for theBenchmark.p
% 49.44/17.47 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------