%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET015-2 : 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 : n009.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 79.24s 12.01s
% Output : CNFRefutation 79.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of clauses : 93 ( 21 unt; 29 nHn; 68 RR)
% Number of literals : 182 ( 0 equ; 55 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 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 : 111 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_union_b_is_c,hypothesis,
'equal$usets'(union(as,bs),cs) ).
cnf(b_union_a_is_d,hypothesis,
'equal$usets'(union(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$u2'(X0,X1),X1) ) ).
cnf(member_of_set1_is_member_of_union,axiom,
( member(X0,union(X1,X2))
| ~ member(X0,X1) ) ).
cnf(member_of_set2_is_member_of_union,axiom,
( member(X0,union(X2,X1))
| ~ member(X0,X1) ) ).
cnf(member_of_union_is_member_of_one_set,axiom,
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ) ).
cnf(set_equal_sets_are_subsets1,axiom,
( subset(X0,X1)
| ~ 'equal$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(symmetry_for_set_equal,axiom,
( 'equal$usets'(X1,X0)
| ~ 'equal$usets'(X0,X1) ) ).
cnf(transitivity_for_set_equal,axiom,
( 'equal$usets'(X0,X2)
| ~ 'equal$usets'(X1,X2)
| ~ 'equal$usets'(X0,X1) ) ).
cnf(c0,plain,
'equal$usets'(union(as,bs),cs),
inference(clausification,[status(esa)],[a_union_b_is_c]) ).
cnf(c1,plain,
'equal$usets'(union(bs,as),ds),
inference(clausification,[status(esa)],[b_union_a_is_d]) ).
cnf(c2,plain,
~ 'equal$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(c9,plain,
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_set1_is_member_of_union]) ).
cnf(c10,plain,
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_set2_is_member_of_union]) ).
cnf(c11,plain,
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[member_of_union_is_member_of_one_set]) ).
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$usets'(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subsets_are_set_equal_sets]) ).
cnf(c19,plain,
( 'equal$usets'(X1,X0)
| ~ 'equal$usets'(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_for_set_equal]) ).
cnf(c20,plain,
( 'equal$usets'(X0,X2)
| ~ 'equal$usets'(X1,X2)
| ~ 'equal$usets'(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_for_set_equal]) ).
cnf(d0,plain,
( ~ 'equal$usets'(X0,union(as,bs))
| 'equal$usets'(X0,cs) ),
inference(resolution,[status(thm)],[c20,c0]) ).
cnf(d1,plain,
( subset(X0,union(X1,X2))
| ~ member('member$uof$u1$unot$uof$u2'(X0,union(X1,X2)),X2) ),
inference(resolution,[status(thm)],[c10,c6]) ).
cnf(d2,plain,
subset(union(as,bs),cs),
inference(resolution,[status(thm)],[c15,c0]) ).
cnf(d3,plain,
( ~ member(X0,union(as,bs))
| member(X0,cs) ),
inference(resolution,[status(thm)],[c4,d2]) ).
cnf(d4,plain,
( subset(union(as,bs),X0)
| member('member$uof$u1$unot$uof$u2'(union(as,bs),X0),cs) ),
inference(resolution,[status(thm)],[d3,c5]) ).
cnf(d5,plain,
( subset(union(as,bs),union(X0,cs))
| subset(union(as,bs),union(X0,cs)) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( ~ subset(union(X0,cs),union(as,bs))
| 'equal$usets'(union(as,bs),union(X0,cs)) ),
inference(resolution,[status(thm)],[d5,c17]) ).
cnf(d7,plain,
subset(cs,union(as,bs)),
inference(resolution,[status(thm)],[c16,c0]) ).
cnf(d8,plain,
( ~ member(X0,cs)
| member(X0,union(as,bs)) ),
inference(resolution,[status(thm)],[c4,d7]) ).
cnf(d9,plain,
( subset(X0,union(as,bs))
| ~ member('member$uof$u1$unot$uof$u2'(X0,union(as,bs)),cs) ),
inference(resolution,[status(thm)],[d8,c6]) ).
cnf(d10,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)],[c11,c5]) ).
cnf(d11,plain,
( subset(union(X0,X1),union(X2,X0))
| subset(union(X0,X1),union(X2,X0))
| member('member$uof$u1$unot$uof$u2'(union(X0,X1),union(X2,X0)),X1) ),
inference(resolution,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
( subset(union(bs,cs),union(as,bs))
| subset(union(bs,cs),union(as,bs)) ),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
'equal$usets'(union(as,bs),union(bs,cs)),
inference(resolution,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
'equal$usets'(union(bs,cs),union(as,bs)),
inference(resolution,[status(thm)],[d13,c19]) ).
cnf(d15,plain,
'equal$usets'(union(bs,cs),cs),
inference(resolution,[status(thm)],[d14,d0]) ).
cnf(d16,plain,
subset(union(bs,cs),cs),
inference(resolution,[status(thm)],[d15,c15]) ).
cnf(d17,plain,
( ~ member(X0,union(bs,cs))
| member(X0,cs) ),
inference(resolution,[status(thm)],[d16,c4]) ).
cnf(d18,plain,
( ~ member(X0,as)
| member(X0,cs) ),
inference(resolution,[status(thm)],[d3,c9]) ).
cnf(d19,plain,
( subset(as,X0)
| member('member$uof$u1$unot$uof$u2'(as,X0),cs) ),
inference(resolution,[status(thm)],[d18,c5]) ).
cnf(d20,plain,
( subset(as,union(X0,cs))
| subset(as,union(X0,cs)) ),
inference(resolution,[status(thm)],[d1,d19]) ).
cnf(d21,plain,
( ~ member(X0,as)
| member(X0,union(X1,cs)) ),
inference(resolution,[status(thm)],[d20,c4]) ).
cnf(d22,plain,
( subset(X0,union(X1,cs))
| ~ member('member$uof$u1$unot$uof$u2'(X0,union(X1,cs)),as) ),
inference(resolution,[status(thm)],[d21,c6]) ).
cnf(d23,plain,
( subset(X0,union(X1,X2))
| ~ member('member$uof$u1$unot$uof$u2'(X0,union(X1,X2)),X1) ),
inference(resolution,[status(thm)],[c9,c6]) ).
cnf(d24,plain,
subset(ds,union(bs,as)),
inference(resolution,[status(thm)],[c16,c1]) ).
cnf(d25,plain,
( ~ member(X0,ds)
| member(X0,union(bs,as)) ),
inference(resolution,[status(thm)],[c4,d24]) ).
cnf(d26,plain,
( ~ member(X0,ds)
| member(X0,bs)
| member(X0,as) ),
inference(resolution,[status(thm)],[c11,d25]) ).
cnf(d27,plain,
( subset(ds,X0)
| member('member$uof$u1$unot$uof$u2'(ds,X0),bs)
| member('member$uof$u1$unot$uof$u2'(ds,X0),as) ),
inference(resolution,[status(thm)],[d26,c5]) ).
cnf(d28,plain,
( subset(ds,union(bs,X0))
| subset(ds,union(bs,X0))
| member('member$uof$u1$unot$uof$u2'(ds,union(bs,X0)),as) ),
inference(resolution,[status(thm)],[d27,d23]) ).
cnf(d29,plain,
( subset(ds,union(bs,cs))
| subset(ds,union(bs,cs)) ),
inference(resolution,[status(thm)],[d28,d22]) ).
cnf(d30,plain,
( ~ member(X0,ds)
| member(X0,union(bs,cs)) ),
inference(resolution,[status(thm)],[d29,c4]) ).
cnf(d31,plain,
( member(X0,cs)
| ~ member(X0,ds) ),
inference(resolution,[status(thm)],[d30,d17]) ).
cnf(d32,plain,
( subset(ds,X0)
| member('member$uof$u1$unot$uof$u2'(ds,X0),cs) ),
inference(resolution,[status(thm)],[d31,c5]) ).
cnf(d33,plain,
( subset(ds,cs)
| subset(ds,cs) ),
inference(resolution,[status(thm)],[d32,c6]) ).
cnf(d34,plain,
( ~ subset(cs,ds)
| 'equal$usets'(ds,cs) ),
inference(resolution,[status(thm)],[d33,c17]) ).
cnf(d35,plain,
( ~ 'equal$usets'(X0,union(bs,as))
| 'equal$usets'(X0,ds) ),
inference(resolution,[status(thm)],[c20,c1]) ).
cnf(d36,plain,
subset(union(bs,as),ds),
inference(resolution,[status(thm)],[c15,c1]) ).
cnf(d37,plain,
( ~ member(X0,union(bs,as))
| member(X0,ds) ),
inference(resolution,[status(thm)],[c4,d36]) ).
cnf(d38,plain,
( subset(union(bs,as),X0)
| member('member$uof$u1$unot$uof$u2'(union(bs,as),X0),ds) ),
inference(resolution,[status(thm)],[d37,c5]) ).
cnf(d39,plain,
( subset(union(bs,as),union(X0,ds))
| subset(union(bs,as),union(X0,ds)) ),
inference(resolution,[status(thm)],[d38,d1]) ).
cnf(d40,plain,
( ~ subset(union(X0,ds),union(bs,as))
| 'equal$usets'(union(bs,as),union(X0,ds)) ),
inference(resolution,[status(thm)],[d39,c17]) ).
cnf(d41,plain,
( subset(X0,union(bs,as))
| ~ member('member$uof$u1$unot$uof$u2'(X0,union(bs,as)),ds) ),
inference(resolution,[status(thm)],[d25,c6]) ).
cnf(d42,plain,
( subset(union(X0,X1),union(X0,X2))
| subset(union(X0,X1),union(X0,X2))
| member('member$uof$u1$unot$uof$u2'(union(X0,X1),union(X0,X2)),X1) ),
inference(resolution,[status(thm)],[d10,d23]) ).
cnf(d43,plain,
( subset(union(bs,ds),union(bs,as))
| subset(union(bs,ds),union(bs,as)) ),
inference(resolution,[status(thm)],[d42,d41]) ).
cnf(d44,plain,
'equal$usets'(union(bs,as),union(bs,ds)),
inference(resolution,[status(thm)],[d43,d40]) ).
cnf(d45,plain,
'equal$usets'(union(bs,ds),union(bs,as)),
inference(resolution,[status(thm)],[d44,c19]) ).
cnf(d46,plain,
'equal$usets'(union(bs,ds),ds),
inference(resolution,[status(thm)],[d45,d35]) ).
cnf(d47,plain,
subset(union(bs,ds),ds),
inference(resolution,[status(thm)],[d46,c15]) ).
cnf(d48,plain,
( ~ member(X0,union(bs,ds))
| member(X0,ds) ),
inference(resolution,[status(thm)],[d47,c4]) ).
cnf(d49,plain,
( ~ member(X0,as)
| member(X0,ds) ),
inference(resolution,[status(thm)],[d37,c10]) ).
cnf(d50,plain,
( subset(as,X0)
| member('member$uof$u1$unot$uof$u2'(as,X0),ds) ),
inference(resolution,[status(thm)],[d49,c5]) ).
cnf(d51,plain,
( subset(as,union(X0,ds))
| subset(as,union(X0,ds)) ),
inference(resolution,[status(thm)],[d1,d50]) ).
cnf(d52,plain,
( ~ member(X0,as)
| member(X0,union(X1,ds)) ),
inference(resolution,[status(thm)],[d51,c4]) ).
cnf(d53,plain,
( subset(X0,union(X1,ds))
| ~ member('member$uof$u1$unot$uof$u2'(X0,union(X1,ds)),as) ),
inference(resolution,[status(thm)],[d52,c6]) ).
cnf(d54,plain,
( ~ member(X0,cs)
| member(X0,as)
| member(X0,bs) ),
inference(resolution,[status(thm)],[c11,d8]) ).
cnf(d55,plain,
( subset(cs,X0)
| member('member$uof$u1$unot$uof$u2'(cs,X0),bs)
| member('member$uof$u1$unot$uof$u2'(cs,X0),as) ),
inference(resolution,[status(thm)],[d54,c5]) ).
cnf(d56,plain,
( subset(cs,union(bs,X0))
| subset(cs,union(bs,X0))
| member('member$uof$u1$unot$uof$u2'(cs,union(bs,X0)),as) ),
inference(resolution,[status(thm)],[d55,d23]) ).
cnf(d57,plain,
( subset(cs,union(bs,ds))
| subset(cs,union(bs,ds)) ),
inference(resolution,[status(thm)],[d56,d53]) ).
cnf(d58,plain,
( ~ member(X0,cs)
| member(X0,union(bs,ds)) ),
inference(resolution,[status(thm)],[d57,c4]) ).
cnf(d59,plain,
( member(X0,ds)
| ~ member(X0,cs) ),
inference(resolution,[status(thm)],[d58,d48]) ).
cnf(d60,plain,
( subset(cs,X0)
| member('member$uof$u1$unot$uof$u2'(cs,X0),ds) ),
inference(resolution,[status(thm)],[d59,c5]) ).
cnf(d61,plain,
( subset(cs,ds)
| subset(cs,ds) ),
inference(resolution,[status(thm)],[d60,c6]) ).
cnf(d62,plain,
'equal$usets'(ds,cs),
inference(resolution,[status(thm)],[d61,d34]) ).
cnf(d63,plain,
'equal$usets'(cs,ds),
inference(resolution,[status(thm)],[d62,c19]) ).
cnf(d64,plain,
$false,
inference(resolution,[status(thm)],[c2,d63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET015-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n009.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 06:50:29 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 79.24/12.01 % SZS status Unsatisfiable for theBenchmark.p
% 79.24/12.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------