%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET012-2 : 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 : 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 08:31:33 AM UTC 2026
% Result : Unsatisfiable 6.07s 4.94s
% Output : CNFRefutation 6.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 43 ( 12 unt; 10 nHn; 35 RR)
% Number of literals : 78 ( 0 equ; 32 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(complement_of_a_is_b,hypothesis,
'equal$usets'(complement(a),b) ).
cnf(complement_of_b_is_c,hypothesis,
'equal$usets'(complement(b),c) ).
cnf(prove_a_equals_c,negated_conjecture,
~ 'equal$usets'(a,c) ).
cnf(membership_in_subsets,axiom,
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ) ).
cnf(subsets_axiom1,axiom,
( member('member$uof$u1$unot$uof$u2'(X0,X1),X0)
| subset(X0,X1) ) ).
cnf(subsets_axiom2,axiom,
( subset(X0,X1)
| ~ member('member$uof$u1$unot$uof$u2'(X0,X1),X1) ) ).
cnf(member_of_set_or_complement,axiom,
( member(X0,complement(X1))
| member(X0,X1) ) ).
cnf(not_member_of_set_and_complement,axiom,
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ) ).
cnf(set_equal_sets_are_subsets1,axiom,
( subset(X0,X1)
| ~ 'equal$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$usets'(complement(a),b),
inference(clausification,[status(esa)],[complement_of_a_is_b]) ).
cnf(c1,plain,
'equal$usets'(complement(b),c),
inference(clausification,[status(esa)],[complement_of_b_is_c]) ).
cnf(c2,plain,
~ 'equal$usets'(a,c),
inference(clausification,[status(esa)],[prove_a_equals_c]) ).
cnf(c4,plain,
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[membership_in_subsets]) ).
cnf(c5,plain,
( member('member$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$u2'(X0,X1),X1) ),
inference(clausification,[status(esa)],[subsets_axiom2]) ).
cnf(c7,plain,
( member(X0,complement(X1))
| member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_set_or_complement]) ).
cnf(c8,plain,
( ~ member(X0,complement(X1))
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[not_member_of_set_and_complement]) ).
cnf(c15,plain,
( subset(X0,X1)
| ~ 'equal$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(b,complement(a)),
inference(resolution,[status(thm)],[c16,c0]) ).
cnf(d1,plain,
( ~ member(X0,b)
| member(X0,complement(a)) ),
inference(resolution,[status(thm)],[c4,d0]) ).
cnf(d2,plain,
( ~ member(X0,a)
| ~ member(X0,b) ),
inference(resolution,[status(thm)],[d1,c8]) ).
cnf(d3,plain,
subset(complement(b),c),
inference(resolution,[status(thm)],[c15,c1]) ).
cnf(d4,plain,
( ~ member(X0,complement(b))
| member(X0,c) ),
inference(resolution,[status(thm)],[c4,d3]) ).
cnf(d5,plain,
( member(X0,b)
| member(X0,c) ),
inference(resolution,[status(thm)],[d4,c7]) ).
cnf(d6,plain,
( member('member$uof$u1$unot$uof$u2'(X0,c),b)
| subset(X0,c) ),
inference(resolution,[status(thm)],[c6,d5]) ).
cnf(d7,plain,
( ~ member('member$uof$u1$unot$uof$u2'(X0,c),a)
| subset(X0,c) ),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( subset(a,c)
| subset(a,c) ),
inference(resolution,[status(thm)],[d7,c5]) ).
cnf(d9,plain,
( ~ subset(c,a)
| 'equal$usets'(a,c) ),
inference(resolution,[status(thm)],[c17,d8]) ).
cnf(d10,plain,
~ subset(c,a),
inference(resolution,[status(thm)],[c2,d9]) ).
cnf(d11,plain,
subset(complement(a),b),
inference(resolution,[status(thm)],[c15,c0]) ).
cnf(d12,plain,
( ~ member(X0,complement(a))
| member(X0,b) ),
inference(resolution,[status(thm)],[c4,d11]) ).
cnf(d13,plain,
( member(X0,a)
| member(X0,b) ),
inference(resolution,[status(thm)],[d12,c7]) ).
cnf(d14,plain,
subset(c,complement(b)),
inference(resolution,[status(thm)],[c16,c1]) ).
cnf(d15,plain,
( ~ member(X0,c)
| member(X0,complement(b)) ),
inference(resolution,[status(thm)],[c4,d14]) ).
cnf(d16,plain,
( ~ member(X0,b)
| ~ member(X0,c) ),
inference(resolution,[status(thm)],[d15,c8]) ).
cnf(d17,plain,
( subset(c,X0)
| ~ member('member$uof$u1$unot$uof$u2'(c,X0),b) ),
inference(resolution,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
( member('member$uof$u1$unot$uof$u2'(c,X0),a)
| subset(c,X0) ),
inference(resolution,[status(thm)],[d17,d13]) ).
cnf(d19,plain,
( subset(c,a)
| subset(c,a) ),
inference(resolution,[status(thm)],[d18,c6]) ).
cnf(d20,plain,
$false,
inference(resolution,[status(thm)],[d19,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET012-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 06:47:08 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.07/4.94 % SZS status Unsatisfiable for theBenchmark.p
% 6.07/4.94 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------