%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET007-1 : 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 : n004.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 08:31:31 AM UTC 2026
% Result : Unsatisfiable 31.73s 10.27s
% Output : CNFRefutation 31.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of clauses : 75 ( 17 unt; 22 nHn; 63 RR)
% Number of literals : 174 ( 0 equ; 66 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-3 aty)
% Number of variables : 104 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_union_c,axiom,
union(b,c,bUc) ).
cnf(a_intersection_b,axiom,
intersection(a,b,aIb) ).
cnf(a_intersection_c,axiom,
intersection(a,c,aIc) ).
cnf(a_intersection_bUc,axiom,
intersection(a,bUc,'aI$ubUc') ).
cnf(prove_aIb_union_aIc_is_aI_bUc,negated_conjecture,
~ union(aIb,aIc,'aI$ubUc') ).
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_union_is_member_of_one_set,axiom,
( member(X3,X1)
| member(X3,X0)
| ~ member(X3,X2)
| ~ union(X0,X1,X2) ) ).
cnf(member_of_set1_is_member_of_union,axiom,
( member(X3,X2)
| ~ member(X3,X0)
| ~ union(X0,X1,X2) ) ).
cnf(member_of_set2_is_member_of_union,axiom,
( member(X3,X2)
| ~ member(X3,X1)
| ~ union(X0,X1,X2) ) ).
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(c0,plain,
union(b,c,bUc),
inference(clausification,[status(esa)],[b_union_c]) ).
cnf(c1,plain,
intersection(a,b,aIb),
inference(clausification,[status(esa)],[a_intersection_b]) ).
cnf(c2,plain,
intersection(a,c,aIc),
inference(clausification,[status(esa)],[a_intersection_c]) ).
cnf(c3,plain,
intersection(a,bUc,'aI$ubUc'),
inference(clausification,[status(esa)],[a_intersection_bUc]) ).
cnf(c4,plain,
~ union(aIb,aIc,'aI$ubUc'),
inference(clausification,[status(esa)],[prove_aIb_union_aIc_is_aI_bUc]) ).
cnf(c5,plain,
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(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(c11,plain,
( member(X3,X1)
| member(X3,X0)
| ~ member(X3,X2)
| ~ union(X0,X1,X2) ),
inference(clausification,[status(esa)],[member_of_union_is_member_of_one_set]) ).
cnf(c12,plain,
( member(X3,X2)
| ~ member(X3,X0)
| ~ union(X0,X1,X2) ),
inference(clausification,[status(esa)],[member_of_set1_is_member_of_union]) ).
cnf(c13,plain,
( member(X3,X2)
| ~ member(X3,X1)
| ~ union(X0,X1,X2) ),
inference(clausification,[status(esa)],[member_of_set2_is_member_of_union]) ).
cnf(c14,plain,
( member(g(X0,X1,X2),X2)
| member(g(X0,X1,X2),X1)
| member(g(X0,X1,X2),X0)
| union(X0,X1,X2) ),
inference(clausification,[status(esa)],[union_axiom1]) ).
cnf(c15,plain,
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X0) ),
inference(clausification,[status(esa)],[union_axiom2]) ).
cnf(c16,plain,
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X1) ),
inference(clausification,[status(esa)],[union_axiom3]) ).
cnf(c17,plain,
( member(X3,X0)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(clausification,[status(esa)],[member_of_intersection_is_member_of_set1]) ).
cnf(c18,plain,
( member(X3,X1)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(clausification,[status(esa)],[member_of_intersection_is_member_of_set2]) ).
cnf(c19,plain,
( member(X3,X2)
| ~ member(X3,X0)
| ~ member(X3,X1)
| ~ intersection(X0,X1,X2) ),
inference(clausification,[status(esa)],[member_of_both_is_member_of_intersection]) ).
cnf(d0,plain,
( ~ member(X0,b)
| ~ member(X0,a)
| member(X0,aIb) ),
inference(resolution,[status(thm)],[c19,c1]) ).
cnf(d1,plain,
( member(X0,a)
| ~ member(X0,aIc) ),
inference(resolution,[status(thm)],[c17,c2]) ).
cnf(d2,plain,
( member(X0,a)
| ~ member(X0,'aI$ubUc') ),
inference(resolution,[status(thm)],[c17,c3]) ).
cnf(d3,plain,
( member(X0,a)
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[c17,c1]) ).
cnf(d4,plain,
( member(g(aIb,X0,X1),X0)
| member(g(aIb,X0,X1),X1)
| union(aIb,X0,X1)
| member(g(aIb,X0,X1),a) ),
inference(resolution,[status(thm)],[d3,c14]) ).
cnf(d5,plain,
( member(g(aIb,X0,'aI$ubUc'),a)
| member(g(aIb,X0,'aI$ubUc'),a)
| member(g(aIb,X0,'aI$ubUc'),X0)
| union(aIb,X0,'aI$ubUc') ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( member(g(aIb,aIc,'aI$ubUc'),a)
| member(g(aIb,aIc,'aI$ubUc'),a)
| union(aIb,aIc,'aI$ubUc') ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
member(g(aIb,aIc,'aI$ubUc'),a),
inference(resolution,[status(thm)],[c4,d6]) ).
cnf(d8,plain,
( member(g(aIb,aIc,'aI$ubUc'),aIb)
| ~ member(g(aIb,aIc,'aI$ubUc'),b) ),
inference(resolution,[status(thm)],[d7,d0]) ).
cnf(d9,plain,
( ~ member(X0,c)
| ~ member(X0,a)
| member(X0,aIc) ),
inference(resolution,[status(thm)],[c19,c2]) ).
cnf(d10,plain,
( member(g(aIb,aIc,'aI$ubUc'),aIc)
| ~ member(g(aIb,aIc,'aI$ubUc'),c) ),
inference(resolution,[status(thm)],[d7,d9]) ).
cnf(d11,plain,
( member(X0,b)
| member(X0,c)
| ~ member(X0,bUc) ),
inference(resolution,[status(thm)],[c11,c0]) ).
cnf(d12,plain,
( ~ member(X0,b)
| member(X0,bUc) ),
inference(resolution,[status(thm)],[c12,c0]) ).
cnf(d13,plain,
( member(X0,b)
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[c18,c1]) ).
cnf(d14,plain,
( subset(aIb,X0)
| member('member$uof$u1$unot$uof$u2'(aIb,X0),b) ),
inference(resolution,[status(thm)],[d13,c6]) ).
cnf(d15,plain,
( member('member$uof$u1$unot$uof$u2'(aIb,X0),bUc)
| subset(aIb,X0) ),
inference(resolution,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
( subset(aIb,bUc)
| subset(aIb,bUc) ),
inference(resolution,[status(thm)],[d15,c7]) ).
cnf(d17,plain,
( ~ member(X0,aIb)
| member(X0,bUc) ),
inference(resolution,[status(thm)],[d16,c5]) ).
cnf(d18,plain,
( ~ member(X0,c)
| member(X0,bUc) ),
inference(resolution,[status(thm)],[c13,c0]) ).
cnf(d19,plain,
( member(X0,c)
| ~ member(X0,aIc) ),
inference(resolution,[status(thm)],[c18,c2]) ).
cnf(d20,plain,
( subset(aIc,X0)
| member('member$uof$u1$unot$uof$u2'(aIc,X0),c) ),
inference(resolution,[status(thm)],[d19,c6]) ).
cnf(d21,plain,
( member('member$uof$u1$unot$uof$u2'(aIc,X0),bUc)
| subset(aIc,X0) ),
inference(resolution,[status(thm)],[d20,d18]) ).
cnf(d22,plain,
( subset(aIc,bUc)
| subset(aIc,bUc) ),
inference(resolution,[status(thm)],[d21,c7]) ).
cnf(d23,plain,
( ~ member(X0,aIc)
| member(X0,bUc) ),
inference(resolution,[status(thm)],[d22,c5]) ).
cnf(d24,plain,
( member(X0,bUc)
| ~ member(X0,'aI$ubUc') ),
inference(resolution,[status(thm)],[c18,c3]) ).
cnf(d25,plain,
( member(g(X0,X1,'aI$ubUc'),X0)
| member(g(X0,X1,'aI$ubUc'),X1)
| union(X0,X1,'aI$ubUc')
| member(g(X0,X1,'aI$ubUc'),bUc) ),
inference(resolution,[status(thm)],[d24,c14]) ).
cnf(d26,plain,
( member(g(X0,aIc,'aI$ubUc'),bUc)
| member(g(X0,aIc,'aI$ubUc'),bUc)
| member(g(X0,aIc,'aI$ubUc'),X0)
| union(X0,aIc,'aI$ubUc') ),
inference(resolution,[status(thm)],[d25,d23]) ).
cnf(d27,plain,
( member(g(aIb,aIc,'aI$ubUc'),bUc)
| member(g(aIb,aIc,'aI$ubUc'),bUc)
| union(aIb,aIc,'aI$ubUc') ),
inference(resolution,[status(thm)],[d26,d17]) ).
cnf(d28,plain,
member(g(aIb,aIc,'aI$ubUc'),bUc),
inference(resolution,[status(thm)],[c4,d27]) ).
cnf(d29,plain,
( member(g(aIb,aIc,'aI$ubUc'),c)
| member(g(aIb,aIc,'aI$ubUc'),b) ),
inference(resolution,[status(thm)],[d28,d11]) ).
cnf(d30,plain,
( member(g(aIb,aIc,'aI$ubUc'),aIc)
| member(g(aIb,aIc,'aI$ubUc'),b) ),
inference(resolution,[status(thm)],[d29,d10]) ).
cnf(d31,plain,
( ~ member(g(aIb,aIc,'aI$ubUc'),'aI$ubUc')
| union(aIb,aIc,'aI$ubUc')
| member(g(aIb,aIc,'aI$ubUc'),b) ),
inference(resolution,[status(thm)],[d30,c16]) ).
cnf(d32,plain,
( ~ member(g(aIb,aIc,'aI$ubUc'),'aI$ubUc')
| member(g(aIb,aIc,'aI$ubUc'),b) ),
inference(resolution,[status(thm)],[c4,d31]) ).
cnf(d33,plain,
( ~ member(X0,bUc)
| ~ member(X0,a)
| member(X0,'aI$ubUc') ),
inference(resolution,[status(thm)],[c19,c3]) ).
cnf(d34,plain,
( member(g(aIb,aIc,'aI$ubUc'),'aI$ubUc')
| ~ member(g(aIb,aIc,'aI$ubUc'),bUc) ),
inference(resolution,[status(thm)],[d7,d33]) ).
cnf(d35,plain,
member(g(aIb,aIc,'aI$ubUc'),'aI$ubUc'),
inference(resolution,[status(thm)],[d28,d34]) ).
cnf(d36,plain,
member(g(aIb,aIc,'aI$ubUc'),b),
inference(resolution,[status(thm)],[d35,d32]) ).
cnf(d37,plain,
member(g(aIb,aIc,'aI$ubUc'),aIb),
inference(resolution,[status(thm)],[d36,d8]) ).
cnf(d38,plain,
( ~ member(g(aIb,aIc,'aI$ubUc'),'aI$ubUc')
| union(aIb,aIc,'aI$ubUc') ),
inference(resolution,[status(thm)],[d37,c15]) ).
cnf(d39,plain,
~ member(g(aIb,aIc,'aI$ubUc'),'aI$ubUc'),
inference(resolution,[status(thm)],[c4,d38]) ).
cnf(d40,plain,
$false,
inference(resolution,[status(thm)],[d35,d39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.39 % Computer : n004.cluster.edu
% 0.09/5.39 % Model : x86_64 x86_64
% 0.09/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.39 % Memory : 8046.5625MB
% 0.09/5.39 % OS : Linux 6.8.0-71-generic
% 0.09/5.39 % CPULimit : 300
% 0.09/5.39 % WCLimit : 300
% 0.09/5.39 % DateTime : Sat Sep 26 06:48:26 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.73/10.27 % SZS status Unsatisfiable for theBenchmark.p
% 31.73/10.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------