%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET002-1 : 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 : 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 08:31:30 AM UTC 2026
% Result : Unsatisfiable 10.34s 1.75s
% Output : CNFRefutation 10.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 23 ( 6 unt; 9 nHn; 19 RR)
% Number of literals : 49 ( 0 equ; 20 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_union_a_is_aUa,hypothesis,
union(a,a,aUa) ).
cnf(prove_a_equals_aUa,negated_conjecture,
~ 'equal$usets'(aUa,a) ).
cnf(subsets_axiom1,axiom,
( member('member$uof$u1$unot$uof$u2'(X0,X1),X0)
| subset(X0,X1) ) ).
cnf(subsets_axiom2,axiom,
( subset(X0,X1)
| ~ member('member$uof$u1$unot$uof$u2'(X0,X1),X1) ) ).
cnf(subsets_are_set_equal_sets,axiom,
( 'equal$usets'(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ).
cnf(member_of_union_is_member_of_one_set,axiom,
( member(X3,X1)
| member(X3,X0)
| ~ member(X3,X2)
| ~ union(X0,X1,X2) ) ).
cnf(member_of_set1_is_member_of_union,axiom,
( member(X3,X2)
| ~ member(X3,X0)
| ~ union(X0,X1,X2) ) ).
cnf(c0,plain,
union(a,a,aUa),
inference(clausification,[status(esa)],[a_union_a_is_aUa]) ).
cnf(c1,plain,
~ 'equal$usets'(aUa,a),
inference(clausification,[status(esa)],[prove_a_equals_aUa]) ).
cnf(c3,plain,
( member('member$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$u2'(X0,X1),X1) ),
inference(clausification,[status(esa)],[subsets_axiom2]) ).
cnf(c7,plain,
( 'equal$usets'(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subsets_are_set_equal_sets]) ).
cnf(c8,plain,
( member(X3,X1)
| member(X3,X0)
| ~ member(X3,X2)
| ~ union(X0,X1,X2) ),
inference(clausification,[status(esa)],[member_of_union_is_member_of_one_set]) ).
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,aUa) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(d1,plain,
( subset(a,X0)
| member('member$uof$u1$unot$uof$u2'(a,X0),aUa) ),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( subset(a,aUa)
| subset(a,aUa) ),
inference(resolution,[status(thm)],[d1,c4]) ).
cnf(d3,plain,
( member(X0,a)
| member(X0,a)
| ~ member(X0,aUa) ),
inference(resolution,[status(thm)],[c8,c0]) ).
cnf(d4,plain,
( subset(aUa,X0)
| member('member$uof$u1$unot$uof$u2'(aUa,X0),a) ),
inference(resolution,[status(thm)],[d3,c3]) ).
cnf(d5,plain,
( subset(aUa,a)
| subset(aUa,a) ),
inference(resolution,[status(thm)],[d4,c4]) ).
cnf(d6,plain,
( ~ subset(a,aUa)
| 'equal$usets'(aUa,a) ),
inference(resolution,[status(thm)],[d5,c7]) ).
cnf(d7,plain,
~ subset(a,aUa),
inference(resolution,[status(thm)],[c1,d6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n006.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 06:47:15 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.34/1.75 % SZS status Unsatisfiable for theBenchmark.p
% 10.34/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------