%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET013-2 : 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 : 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 08:31:33 AM UTC 2026
% Result : Unsatisfiable 23.16s 13.36s
% Output : CNFRefutation 23.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of clauses : 51 ( 12 unt; 12 nHn; 43 RR)
% Number of literals : 102 ( 0 equ; 40 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 62 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(intersection_of_a_and_b_is_c,hypothesis,
'equal$usets'(intersection(as,bs),cs) ).
cnf(intersection_of_b_and_a_is_d,hypothesis,
'equal$usets'(intersection(bs,as),ds) ).
cnf(prove_c_equals_d,negated_conjecture,
~ 'equal$usets'(cs,ds) ).
cnf(membership_in_subsets,axiom,
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ) ).
cnf(subsets_axiom1,axiom,
( member('member$uof$u1$unot$uof$u2'(X0,X1),X0)
| subset(X0,X1) ) ).
cnf(subsets_axiom2,axiom,
( subset(X0,X1)
| ~ member('member$uof$u1$unot$uof$u2'(X0,X1),X1) ) ).
cnf(member_of_both_is_member_of_intersection,axiom,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ) ).
cnf(member_of_intersection_is_member_of_set1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(member_of_intersection_is_member_of_set2,axiom,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(set_equal_sets_are_subsets1,axiom,
( subset(X0,X1)
| ~ 'equal$usets'(X0,X1) ) ).
cnf(set_equal_sets_are_subsets2,axiom,
( subset(X1,X0)
| ~ 'equal$usets'(X0,X1) ) ).
cnf(subsets_are_set_equal_sets,axiom,
( 'equal$usets'(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ).
cnf(c0,plain,
'equal$usets'(intersection(as,bs),cs),
inference(clausification,[status(esa)],[intersection_of_a_and_b_is_c]) ).
cnf(c1,plain,
'equal$usets'(intersection(bs,as),ds),
inference(clausification,[status(esa)],[intersection_of_b_and_a_is_d]) ).
cnf(c2,plain,
~ 'equal$usets'(cs,ds),
inference(clausification,[status(esa)],[prove_c_equals_d]) ).
cnf(c4,plain,
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[membership_in_subsets]) ).
cnf(c5,plain,
( member('member$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$u2'(X0,X1),X1) ),
inference(clausification,[status(esa)],[subsets_axiom2]) ).
cnf(c12,plain,
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_both_is_member_of_intersection]) ).
cnf(c13,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[member_of_intersection_is_member_of_set1]) ).
cnf(c14,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[member_of_intersection_is_member_of_set2]) ).
cnf(c15,plain,
( subset(X0,X1)
| ~ 'equal$usets'(X0,X1) ),
inference(clausification,[status(esa)],[set_equal_sets_are_subsets1]) ).
cnf(c16,plain,
( subset(X1,X0)
| ~ 'equal$usets'(X0,X1) ),
inference(clausification,[status(esa)],[set_equal_sets_are_subsets2]) ).
cnf(c17,plain,
( 'equal$usets'(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subsets_are_set_equal_sets]) ).
cnf(d0,plain,
subset(ds,intersection(bs,as)),
inference(resolution,[status(thm)],[c16,c1]) ).
cnf(d1,plain,
( ~ member(X0,ds)
| member(X0,intersection(bs,as)) ),
inference(resolution,[status(thm)],[c4,d0]) ).
cnf(d2,plain,
( member(X0,as)
| ~ member(X0,ds) ),
inference(resolution,[status(thm)],[d1,c14]) ).
cnf(d3,plain,
( subset(ds,X0)
| member('member$uof$u1$unot$uof$u2'(ds,X0),as) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
( member(X0,bs)
| ~ member(X0,ds) ),
inference(resolution,[status(thm)],[d1,c13]) ).
cnf(d5,plain,
( subset(ds,X0)
| member('member$uof$u1$unot$uof$u2'(ds,X0),bs) ),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
subset(intersection(as,bs),cs),
inference(resolution,[status(thm)],[c15,c0]) ).
cnf(d7,plain,
( ~ member(X0,intersection(as,bs))
| member(X0,cs) ),
inference(resolution,[status(thm)],[c4,d6]) ).
cnf(d8,plain,
( member(X0,cs)
| ~ member(X0,bs)
| ~ member(X0,as) ),
inference(resolution,[status(thm)],[c12,d7]) ).
cnf(d9,plain,
( subset(ds,X0)
| member('member$uof$u1$unot$uof$u2'(ds,X0),cs)
| ~ member('member$uof$u1$unot$uof$u2'(ds,X0),as) ),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( subset(ds,X0)
| subset(ds,X0)
| member('member$uof$u1$unot$uof$u2'(ds,X0),cs) ),
inference(resolution,[status(thm)],[d9,d3]) ).
cnf(d11,plain,
( subset(ds,cs)
| subset(ds,cs) ),
inference(resolution,[status(thm)],[d10,c6]) ).
cnf(d12,plain,
subset(cs,intersection(as,bs)),
inference(resolution,[status(thm)],[c16,c0]) ).
cnf(d13,plain,
( ~ member(X0,cs)
| member(X0,intersection(as,bs)) ),
inference(resolution,[status(thm)],[c4,d12]) ).
cnf(d14,plain,
( member(X0,as)
| ~ member(X0,cs) ),
inference(resolution,[status(thm)],[d13,c13]) ).
cnf(d15,plain,
( subset(cs,X0)
| member('member$uof$u1$unot$uof$u2'(cs,X0),as) ),
inference(resolution,[status(thm)],[d14,c5]) ).
cnf(d16,plain,
( member(X0,bs)
| ~ member(X0,cs) ),
inference(resolution,[status(thm)],[d13,c14]) ).
cnf(d17,plain,
( subset(cs,X0)
| member('member$uof$u1$unot$uof$u2'(cs,X0),bs) ),
inference(resolution,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
subset(intersection(bs,as),ds),
inference(resolution,[status(thm)],[c15,c1]) ).
cnf(d19,plain,
( ~ member(X0,intersection(bs,as))
| member(X0,ds) ),
inference(resolution,[status(thm)],[c4,d18]) ).
cnf(d20,plain,
( member(X0,ds)
| ~ member(X0,as)
| ~ member(X0,bs) ),
inference(resolution,[status(thm)],[c12,d19]) ).
cnf(d21,plain,
( subset(cs,X0)
| member('member$uof$u1$unot$uof$u2'(cs,X0),ds)
| ~ member('member$uof$u1$unot$uof$u2'(cs,X0),as) ),
inference(resolution,[status(thm)],[d20,d17]) ).
cnf(d22,plain,
( subset(cs,X0)
| subset(cs,X0)
| member('member$uof$u1$unot$uof$u2'(cs,X0),ds) ),
inference(resolution,[status(thm)],[d21,d15]) ).
cnf(d23,plain,
( subset(cs,ds)
| subset(cs,ds) ),
inference(resolution,[status(thm)],[d22,c6]) ).
cnf(d24,plain,
( ~ subset(ds,cs)
| 'equal$usets'(cs,ds) ),
inference(resolution,[status(thm)],[d23,c17]) ).
cnf(d25,plain,
~ subset(ds,cs),
inference(resolution,[status(thm)],[c2,d24]) ).
cnf(d26,plain,
$false,
inference(resolution,[status(thm)],[d25,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET013-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n006.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Sat Sep 26 06:49:40 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.16/13.36 % SZS status Unsatisfiable for theBenchmark.p
% 23.16/13.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------