%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET012-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 08:31:32 AM UTC 2026
% Result : Unsatisfiable 8.41s 3.35s
% Output : CNFRefutation 8.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 24 ( 5 unt; 8 nHn; 14 RR)
% Number of literals : 45 ( 0 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_involution,negated_conjecture,
~ 'equal$usets'(complement(complement(a)),a) ).
cnf(subsets_axiom1,axiom,
( member('member$uof$u1$unot$uof$u2'(X0,X1),X0)
| subset(X0,X1) ) ).
cnf(subsets_axiom2,axiom,
( subset(X0,X1)
| ~ member('member$uof$u1$unot$uof$u2'(X0,X1),X1) ) ).
cnf(member_of_set_or_complement,axiom,
( member(X0,complement(X1))
| member(X0,X1) ) ).
cnf(not_member_of_set_and_complement,axiom,
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ) ).
cnf(subsets_are_set_equal_sets,axiom,
( 'equal$usets'(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ).
cnf(symmetry_for_set_equal,axiom,
( 'equal$usets'(X1,X0)
| ~ 'equal$usets'(X0,X1) ) ).
cnf(c0,plain,
~ 'equal$usets'(complement(complement(a)),a),
inference(clausification,[status(esa)],[prove_involution]) ).
cnf(c3,plain,
( member('member$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$u2'(X0,X1),X1) ),
inference(clausification,[status(esa)],[subsets_axiom2]) ).
cnf(c5,plain,
( member(X0,complement(X1))
| member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_set_or_complement]) ).
cnf(c6,plain,
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[not_member_of_set_and_complement]) ).
cnf(c15,plain,
( 'equal$usets'(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subsets_are_set_equal_sets]) ).
cnf(c17,plain,
( 'equal$usets'(X1,X0)
| ~ 'equal$usets'(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_for_set_equal]) ).
cnf(d0,plain,
( subset(X0,complement(X1))
| member('member$uof$u1$unot$uof$u2'(X0,complement(X1)),X1) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(d1,plain,
( ~ member('member$uof$u1$unot$uof$u2'(X0,complement(complement(X1))),X1)
| subset(X0,complement(complement(X1))) ),
inference(resolution,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
( subset(X0,complement(complement(X0)))
| subset(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
( ~ subset(complement(complement(X0)),X0)
| 'equal$usets'(X0,complement(complement(X0))) ),
inference(resolution,[status(thm)],[d2,c15]) ).
cnf(d4,plain,
( subset(complement(X0),X1)
| ~ member('member$uof$u1$unot$uof$u2'(complement(X0),X1),X0) ),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d5,plain,
( member('member$uof$u1$unot$uof$u2'(complement(complement(X0)),X1),X0)
| subset(complement(complement(X0)),X1) ),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
( subset(complement(complement(X0)),X0)
| subset(complement(complement(X0)),X0) ),
inference(resolution,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
'equal$usets'(X0,complement(complement(X0))),
inference(resolution,[status(thm)],[d6,d3]) ).
cnf(d8,plain,
'equal$usets'(complement(complement(X0)),X0),
inference(resolution,[status(thm)],[d7,c17]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET012-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n006.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 06:49:10 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.41/3.35 % SZS status Unsatisfiable for theBenchmark.p
% 8.41/3.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------