%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 10.66s 3.06s
% Output : CNFRefutation 10.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 32 ( 11 unt; 8 nHn; 28 RR)
% Number of literals : 66 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 45 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d_is_a_subset_of_a,hypothesis,
subset(d,a) ).
cnf(b_minus_a,hypothesis,
difference(b,a,bDa) ).
cnf(b_minus_d,hypothesis,
difference(b,d,bDd) ).
cnf(prove_bDa_is_a_subset_of_bDd,negated_conjecture,
~ subset(bDa,bDd) ).
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_difference,axiom,
( member(X3,X0)
| ~ member(X3,X2)
| ~ difference(X0,X1,X2) ) ).
cnf(not_member_of_difference,axiom,
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ) ).
cnf(member_of_difference_or_set2,axiom,
( member(X0,X2)
| member(X0,X3)
| ~ difference(X1,X2,X3)
| ~ member(X0,X1) ) ).
cnf(c0,plain,
subset(d,a),
inference(clausification,[status(esa)],[d_is_a_subset_of_a]) ).
cnf(c1,plain,
difference(b,a,bDa),
inference(clausification,[status(esa)],[b_minus_a]) ).
cnf(c2,plain,
difference(b,d,bDd),
inference(clausification,[status(esa)],[b_minus_d]) ).
cnf(c3,plain,
~ subset(bDa,bDd),
inference(clausification,[status(esa)],[prove_bDa_is_a_subset_of_bDd]) ).
cnf(c4,plain,
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(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(c10,plain,
( member(X3,X0)
| ~ member(X3,X2)
| ~ difference(X0,X1,X2) ),
inference(clausification,[status(esa)],[member_of_difference]) ).
cnf(c11,plain,
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[not_member_of_difference]) ).
cnf(c12,plain,
( member(X0,X2)
| member(X0,X3)
| ~ difference(X1,X2,X3)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_difference_or_set2]) ).
cnf(d0,plain,
( ~ member(X0,a)
| ~ member(X0,bDa) ),
inference(resolution,[status(thm)],[c11,c1]) ).
cnf(d1,plain,
( subset(bDa,X0)
| ~ member('member$uof$u1$unot$uof$u2'(bDa,X0),a) ),
inference(resolution,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
( ~ member(X0,b)
| member(X0,d)
| member(X0,bDd) ),
inference(resolution,[status(thm)],[c12,c2]) ).
cnf(d3,plain,
( member(X0,b)
| ~ member(X0,bDa) ),
inference(resolution,[status(thm)],[c10,c1]) ).
cnf(d4,plain,
( subset(bDa,X0)
| member('member$uof$u1$unot$uof$u2'(bDa,X0),b) ),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
( member('member$uof$u1$unot$uof$u2'(bDa,X0),bDd)
| member('member$uof$u1$unot$uof$u2'(bDa,X0),d)
| subset(bDa,X0) ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( subset(bDa,bDd)
| member('member$uof$u1$unot$uof$u2'(bDa,bDd),d)
| subset(bDa,bDd) ),
inference(resolution,[status(thm)],[d5,c6]) ).
cnf(d7,plain,
member('member$uof$u1$unot$uof$u2'(bDa,bDd),d),
inference(resolution,[status(thm)],[c3,d6]) ).
cnf(d8,plain,
( member('member$uof$u1$unot$uof$u2'(bDa,bDd),X0)
| ~ subset(d,X0) ),
inference(resolution,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
( subset(bDa,bDd)
| ~ subset(d,a) ),
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
subset(bDa,bDd),
inference(resolution,[status(thm)],[c0,d9]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[c3,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 06:46:53 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.66/3.06 % SZS status Unsatisfiable for theBenchmark.p
% 10.66/3.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------