%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET010-1 : 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 : 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 08:31:32 AM UTC 2026
% Result : Unsatisfiable 30.89s 4.59s
% Output : CNFRefutation 30.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of clauses : 73 ( 18 unt; 24 nHn; 65 RR)
% Number of literals : 167 ( 0 equ; 69 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 98 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_intersection_b,hypothesis,
intersection(a,b,aIb) ).
cnf(c_minus_a,hypothesis,
difference(c,a,cDa) ).
cnf(c_minus_b,hypothesis,
difference(c,b,cDb) ).
cnf(c_minus_aIb,hypothesis,
difference(c,aIb,'cD$uaIb') ).
cnf(prove_cDa_union_cDb_is_cD_aIb,negated_conjecture,
~ union(cDa,cDb,'cD$uaIb') ).
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(union_axiom1,axiom,
( member(g(X0,X1,X2),X2)
| member(g(X0,X1,X2),X1)
| member(g(X0,X1,X2),X0)
| union(X0,X1,X2) ) ).
cnf(union_axiom2,axiom,
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X0) ) ).
cnf(union_axiom3,axiom,
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X1) ) ).
cnf(member_of_intersection_is_member_of_set1,axiom,
( member(X3,X0)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ) ).
cnf(member_of_intersection_is_member_of_set2,axiom,
( member(X3,X1)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ) ).
cnf(member_of_both_is_member_of_intersection,axiom,
( member(X3,X2)
| ~ member(X3,X0)
| ~ member(X3,X1)
| ~ intersection(X0,X1,X2) ) ).
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,
intersection(a,b,aIb),
inference(clausification,[status(esa)],[a_intersection_b]) ).
cnf(c1,plain,
difference(c,a,cDa),
inference(clausification,[status(esa)],[c_minus_a]) ).
cnf(c2,plain,
difference(c,b,cDb),
inference(clausification,[status(esa)],[c_minus_b]) ).
cnf(c3,plain,
difference(c,aIb,'cD$uaIb'),
inference(clausification,[status(esa)],[c_minus_aIb]) ).
cnf(c4,plain,
~ union(cDa,cDb,'cD$uaIb'),
inference(clausification,[status(esa)],[prove_cDa_union_cDb_is_cD_aIb]) ).
cnf(c5,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[membership_in_subsets]) ).
cnf(c6,plain,
( member('member$uof$u1$unot$uof$u2'(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subsets_axiom1]) ).
cnf(c7,plain,
( subset(X0,X1)
| ~ member('member$uof$u1$unot$uof$u2'(X0,X1),X1) ),
inference(clausification,[status(esa)],[subsets_axiom2]) ).
cnf(c14,plain,
( member(g(X0,X1,X2),X2)
| member(g(X0,X1,X2),X0)
| union(X0,X1,X2)
| member(g(X0,X1,X2),X1) ),
inference(clausification,[status(esa)],[union_axiom1]) ).
cnf(c15,plain,
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X0)
| ~ member(g(X0,X1,X2),X2) ),
inference(clausification,[status(esa)],[union_axiom2]) ).
cnf(c16,plain,
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X1)
| ~ member(g(X0,X1,X2),X2) ),
inference(clausification,[status(esa)],[union_axiom3]) ).
cnf(c17,plain,
( member(X0,X2)
| ~ intersection(X2,X3,X1)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_intersection_is_member_of_set1]) ).
cnf(c18,plain,
( member(X0,X3)
| ~ intersection(X2,X3,X1)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_intersection_is_member_of_set2]) ).
cnf(c19,plain,
( member(X0,X3)
| ~ member(X0,X2)
| ~ intersection(X1,X2,X3)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_both_is_member_of_intersection]) ).
cnf(c23,plain,
( member(X0,X2)
| ~ difference(X2,X3,X1)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_difference]) ).
cnf(c24,plain,
( ~ difference(X3,X2,X1)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[not_member_of_difference]) ).
cnf(c25,plain,
( member(X0,X3)
| ~ difference(X2,X3,X1)
| ~ member(X0,X2)
| member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_difference_or_set2]) ).
cnf(d0,plain,
( ~ member(X0,'cD$uaIb')
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[c24,c3]) ).
cnf(d1,plain,
( ~ member(X0,b)
| ~ member(X0,a)
| member(X0,aIb) ),
inference(resolution,[status(thm)],[c19,c0]) ).
cnf(d2,plain,
( ~ member(X0,c)
| member(X0,a)
| member(X0,cDa) ),
inference(resolution,[status(thm)],[c25,c1]) ).
cnf(d3,plain,
( member(X0,c)
| ~ member(X0,'cD$uaIb') ),
inference(resolution,[status(thm)],[c23,c3]) ).
cnf(d4,plain,
( member(g(cDa,cDb,'cD$uaIb'),cDa)
| member(g(cDa,cDb,'cD$uaIb'),cDb)
| member(g(cDa,cDb,'cD$uaIb'),'cD$uaIb') ),
inference(resolution,[status(thm)],[c14,c4]) ).
cnf(d5,plain,
( ~ subset(cDa,X0)
| member(g(cDa,cDb,'cD$uaIb'),X0)
| member(g(cDa,cDb,'cD$uaIb'),'cD$uaIb')
| member(g(cDa,cDb,'cD$uaIb'),cDb) ),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
( ~ member(X0,cDa)
| ~ member(X0,a) ),
inference(resolution,[status(thm)],[c24,c1]) ).
cnf(d7,plain,
( member(X0,a)
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[c17,c0]) ).
cnf(d8,plain,
( member(X0,c)
| ~ member(X0,cDa) ),
inference(resolution,[status(thm)],[c23,c1]) ).
cnf(d9,plain,
( subset(cDa,X0)
| member('member$uof$u1$unot$uof$u2'(cDa,X0),c) ),
inference(resolution,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
( ~ member(X0,c)
| member(X0,aIb)
| member(X0,'cD$uaIb') ),
inference(resolution,[status(thm)],[c25,c3]) ).
cnf(d11,plain,
( subset(cDa,X0)
| member('member$uof$u1$unot$uof$u2'(cDa,X0),'cD$uaIb')
| member('member$uof$u1$unot$uof$u2'(cDa,X0),aIb) ),
inference(resolution,[status(thm)],[d10,d9]) ).
cnf(d12,plain,
( member('member$uof$u1$unot$uof$u2'(cDa,X0),a)
| subset(cDa,X0)
| member('member$uof$u1$unot$uof$u2'(cDa,X0),'cD$uaIb') ),
inference(resolution,[status(thm)],[d11,d7]) ).
cnf(d13,plain,
( ~ member('member$uof$u1$unot$uof$u2'(cDa,X0),cDa)
| subset(cDa,X0)
| member('member$uof$u1$unot$uof$u2'(cDa,X0),'cD$uaIb') ),
inference(resolution,[status(thm)],[d12,d6]) ).
cnf(d14,plain,
( subset(cDa,X0)
| subset(cDa,X0)
| member('member$uof$u1$unot$uof$u2'(cDa,X0),'cD$uaIb') ),
inference(resolution,[status(thm)],[d13,c6]) ).
cnf(d15,plain,
( subset(cDa,'cD$uaIb')
| subset(cDa,'cD$uaIb') ),
inference(resolution,[status(thm)],[d14,c7]) ).
cnf(d16,plain,
( member(g(cDa,cDb,'cD$uaIb'),'cD$uaIb')
| member(g(cDa,cDb,'cD$uaIb'),cDb)
| member(g(cDa,cDb,'cD$uaIb'),'cD$uaIb') ),
inference(resolution,[status(thm)],[d15,d5]) ).
cnf(d17,plain,
( ~ member(X0,cDb)
| ~ member(X0,b) ),
inference(resolution,[status(thm)],[c24,c2]) ).
cnf(d18,plain,
( member(X0,b)
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[c18,c0]) ).
cnf(d19,plain,
( member(X0,c)
| ~ member(X0,cDb) ),
inference(resolution,[status(thm)],[c23,c2]) ).
cnf(d20,plain,
( member(g(cDa,cDb,'cD$uaIb'),c)
| member(g(cDa,cDb,'cD$uaIb'),'cD$uaIb') ),
inference(resolution,[status(thm)],[d16,d19]) ).
cnf(d21,plain,
( member(g(cDa,cDb,'cD$uaIb'),'cD$uaIb')
| member(g(cDa,cDb,'cD$uaIb'),aIb)
| member(g(cDa,cDb,'cD$uaIb'),'cD$uaIb') ),
inference(resolution,[status(thm)],[d20,d10]) ).
cnf(d22,plain,
( member(g(cDa,cDb,'cD$uaIb'),b)
| member(g(cDa,cDb,'cD$uaIb'),'cD$uaIb') ),
inference(resolution,[status(thm)],[d21,d18]) ).
cnf(d23,plain,
( ~ member(g(cDa,cDb,'cD$uaIb'),cDb)
| member(g(cDa,cDb,'cD$uaIb'),'cD$uaIb') ),
inference(resolution,[status(thm)],[d22,d17]) ).
cnf(d24,plain,
( member(g(cDa,cDb,'cD$uaIb'),'cD$uaIb')
| member(g(cDa,cDb,'cD$uaIb'),'cD$uaIb') ),
inference(resolution,[status(thm)],[d23,d16]) ).
cnf(d25,plain,
member(g(cDa,cDb,'cD$uaIb'),c),
inference(resolution,[status(thm)],[d24,d3]) ).
cnf(d26,plain,
( member(g(cDa,cDb,'cD$uaIb'),cDa)
| member(g(cDa,cDb,'cD$uaIb'),a) ),
inference(resolution,[status(thm)],[d25,d2]) ).
cnf(d27,plain,
( ~ member(g(cDa,cDb,'cD$uaIb'),cDa)
| union(cDa,cDb,'cD$uaIb') ),
inference(resolution,[status(thm)],[d24,c15]) ).
cnf(d28,plain,
~ member(g(cDa,cDb,'cD$uaIb'),cDa),
inference(resolution,[status(thm)],[c4,d27]) ).
cnf(d29,plain,
member(g(cDa,cDb,'cD$uaIb'),a),
inference(resolution,[status(thm)],[d28,d26]) ).
cnf(d30,plain,
( member(g(cDa,cDb,'cD$uaIb'),aIb)
| ~ member(g(cDa,cDb,'cD$uaIb'),b) ),
inference(resolution,[status(thm)],[d29,d1]) ).
cnf(d31,plain,
( ~ member(X0,c)
| member(X0,b)
| member(X0,cDb) ),
inference(resolution,[status(thm)],[c25,c2]) ).
cnf(d32,plain,
( member(g(cDa,cDb,'cD$uaIb'),cDb)
| member(g(cDa,cDb,'cD$uaIb'),b) ),
inference(resolution,[status(thm)],[d25,d31]) ).
cnf(d33,plain,
( ~ member(g(cDa,cDb,'cD$uaIb'),cDb)
| union(cDa,cDb,'cD$uaIb') ),
inference(resolution,[status(thm)],[d24,c16]) ).
cnf(d34,plain,
~ member(g(cDa,cDb,'cD$uaIb'),cDb),
inference(resolution,[status(thm)],[c4,d33]) ).
cnf(d35,plain,
member(g(cDa,cDb,'cD$uaIb'),b),
inference(resolution,[status(thm)],[d34,d32]) ).
cnf(d36,plain,
member(g(cDa,cDb,'cD$uaIb'),aIb),
inference(resolution,[status(thm)],[d35,d30]) ).
cnf(d37,plain,
~ member(g(cDa,cDb,'cD$uaIb'),'cD$uaIb'),
inference(resolution,[status(thm)],[d36,d0]) ).
cnf(d38,plain,
$false,
inference(resolution,[status(thm)],[d24,d37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 06:48:59 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.89/4.59 % SZS status Unsatisfiable for theBenchmark.p
% 30.89/4.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------