%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET005-1 : 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 : n014.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 16.03s 7.74s
% Output : CNFRefutation 16.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 13
% Syntax : Number of clauses : 60 ( 14 unt; 20 nHn; 46 RR)
% Number of literals : 138 ( 0 equ; 50 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-3 aty)
% Number of variables : 80 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_intersection_b,axiom,
intersection(a,b,aIb) ).
cnf(b_intersection_c,axiom,
intersection(b,c,bIc) ).
cnf(a_intersection_bIc,axiom,
intersection(a,bIc,aIbIc) ).
cnf(prove_aIb_intersection_c_is_aIbIc,negated_conjecture,
~ intersection(aIb,c,aIbIc) ).
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_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(intersection_axiom1,axiom,
( member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ) ).
cnf(intersection_axiom2,axiom,
( member(h(X0,X1,X2),X1)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ) ).
cnf(intersection_axiom3,axiom,
( intersection(X0,X1,X2)
| ~ member(h(X0,X1,X2),X0)
| ~ member(h(X0,X1,X2),X1)
| ~ member(h(X0,X1,X2),X2) ) ).
cnf(c0,plain,
intersection(a,b,aIb),
inference(clausification,[status(esa)],[a_intersection_b]) ).
cnf(c1,plain,
intersection(b,c,bIc),
inference(clausification,[status(esa)],[b_intersection_c]) ).
cnf(c2,plain,
intersection(a,bIc,aIbIc),
inference(clausification,[status(esa)],[a_intersection_bIc]) ).
cnf(c3,plain,
~ intersection(aIb,c,aIbIc),
inference(clausification,[status(esa)],[prove_aIb_intersection_c_is_aIbIc]) ).
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(c10,plain,
( member(X3,X0)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(clausification,[status(esa)],[member_of_intersection_is_member_of_set1]) ).
cnf(c11,plain,
( member(X3,X1)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(clausification,[status(esa)],[member_of_intersection_is_member_of_set2]) ).
cnf(c12,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(c13,plain,
( member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(clausification,[status(esa)],[intersection_axiom1]) ).
cnf(c14,plain,
( member(h(X0,X1,X2),X1)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(clausification,[status(esa)],[intersection_axiom2]) ).
cnf(c15,plain,
( intersection(X0,X1,X2)
| ~ member(h(X0,X1,X2),X0)
| ~ member(h(X0,X1,X2),X1)
| ~ member(h(X0,X1,X2),X2) ),
inference(clausification,[status(esa)],[intersection_axiom3]) ).
cnf(d0,plain,
( member(X0,a)
| ~ member(X0,aIbIc) ),
inference(resolution,[status(thm)],[c10,c2]) ).
cnf(d1,plain,
( subset(aIbIc,X0)
| member('member$uof$u1$unot$uof$u2'(aIbIc,X0),a) ),
inference(resolution,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
( ~ member(X0,b)
| ~ member(X0,a)
| member(X0,aIb) ),
inference(resolution,[status(thm)],[c12,c0]) ).
cnf(d3,plain,
( member(X0,b)
| ~ member(X0,bIc) ),
inference(resolution,[status(thm)],[c10,c1]) ).
cnf(d4,plain,
( ~ member(X0,aIbIc)
| member(X0,bIc) ),
inference(resolution,[status(thm)],[c11,c2]) ).
cnf(d5,plain,
( subset(aIbIc,X0)
| member('member$uof$u1$unot$uof$u2'(aIbIc,X0),bIc) ),
inference(resolution,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
( member('member$uof$u1$unot$uof$u2'(aIbIc,X0),b)
| subset(aIbIc,X0) ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( member('member$uof$u1$unot$uof$u2'(aIbIc,X0),aIb)
| ~ member('member$uof$u1$unot$uof$u2'(aIbIc,X0),a)
| subset(aIbIc,X0) ),
inference(resolution,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( subset(aIbIc,X0)
| subset(aIbIc,X0)
| member('member$uof$u1$unot$uof$u2'(aIbIc,X0),aIb) ),
inference(resolution,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
( subset(aIbIc,aIb)
| subset(aIbIc,aIb) ),
inference(resolution,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
( ~ member(X0,aIbIc)
| member(X0,aIb) ),
inference(resolution,[status(thm)],[d9,c4]) ).
cnf(d11,plain,
( member(X0,a)
| ~ member(X0,aIb) ),
inference(resolution,[status(thm)],[c10,c0]) ).
cnf(d12,plain,
( member(h(aIb,X0,X1),X1)
| intersection(aIb,X0,X1)
| member(h(aIb,X0,X1),a) ),
inference(resolution,[status(thm)],[d11,c13]) ).
cnf(d13,plain,
( ~ member(X0,bIc)
| ~ member(X0,a)
| member(X0,aIbIc) ),
inference(resolution,[status(thm)],[c12,c2]) ).
cnf(d14,plain,
( ~ member(X0,aIb)
| member(X0,b) ),
inference(resolution,[status(thm)],[c11,c0]) ).
cnf(d15,plain,
( member(h(aIb,X0,X1),X1)
| intersection(aIb,X0,X1)
| member(h(aIb,X0,X1),b) ),
inference(resolution,[status(thm)],[d14,c13]) ).
cnf(d16,plain,
( subset(aIbIc,b)
| subset(aIbIc,b) ),
inference(resolution,[status(thm)],[d6,c6]) ).
cnf(d17,plain,
( ~ member(X0,aIbIc)
| member(X0,b) ),
inference(resolution,[status(thm)],[d16,c4]) ).
cnf(d18,plain,
( member(h(aIb,X0,aIbIc),b)
| intersection(aIb,X0,aIbIc)
| member(h(aIb,X0,aIbIc),b) ),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
( ~ member(X0,c)
| ~ member(X0,b)
| member(X0,bIc) ),
inference(resolution,[status(thm)],[c12,c1]) ).
cnf(d20,plain,
( member(h(X0,X1,aIbIc),X1)
| intersection(X0,X1,aIbIc)
| member(h(X0,X1,aIbIc),bIc) ),
inference(resolution,[status(thm)],[d4,c14]) ).
cnf(d21,plain,
( member(h(X0,c,aIbIc),bIc)
| ~ member(h(X0,c,aIbIc),b)
| member(h(X0,c,aIbIc),bIc)
| intersection(X0,c,aIbIc) ),
inference(resolution,[status(thm)],[d20,d19]) ).
cnf(d22,plain,
( intersection(aIb,c,aIbIc)
| member(h(aIb,c,aIbIc),bIc)
| intersection(aIb,c,aIbIc) ),
inference(resolution,[status(thm)],[d21,d18]) ).
cnf(d23,plain,
member(h(aIb,c,aIbIc),bIc),
inference(resolution,[status(thm)],[c3,d22]) ).
cnf(d24,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| ~ member(h(aIb,c,aIbIc),a) ),
inference(resolution,[status(thm)],[d23,d13]) ).
cnf(d25,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| intersection(aIb,c,aIbIc)
| member(h(aIb,c,aIbIc),aIbIc) ),
inference(resolution,[status(thm)],[d24,d12]) ).
cnf(d26,plain,
member(h(aIb,c,aIbIc),aIbIc),
inference(resolution,[status(thm)],[c3,d25]) ).
cnf(d27,plain,
member(h(aIb,c,aIbIc),aIb),
inference(resolution,[status(thm)],[d26,d10]) ).
cnf(d28,plain,
( ~ member(h(aIb,c,aIbIc),c)
| ~ member(h(aIb,c,aIbIc),aIbIc)
| intersection(aIb,c,aIbIc) ),
inference(resolution,[status(thm)],[d27,c15]) ).
cnf(d29,plain,
( ~ member(h(aIb,c,aIbIc),aIbIc)
| ~ member(h(aIb,c,aIbIc),c) ),
inference(resolution,[status(thm)],[c3,d28]) ).
cnf(d30,plain,
( ~ member(X0,bIc)
| member(X0,c) ),
inference(resolution,[status(thm)],[c11,c1]) ).
cnf(d31,plain,
member(h(aIb,c,aIbIc),c),
inference(resolution,[status(thm)],[d23,d30]) ).
cnf(d32,plain,
~ member(h(aIb,c,aIbIc),aIbIc),
inference(resolution,[status(thm)],[d31,d29]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d26,d32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/5.36 % Computer : n014.cluster.edu
% 0.07/5.36 % Model : x86_64 x86_64
% 0.07/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.36 % Memory : 8046.5625MB
% 0.07/5.36 % OS : Linux 6.8.0-71-generic
% 0.07/5.36 % CPULimit : 300
% 0.07/5.36 % WCLimit : 300
% 0.07/5.36 % DateTime : Sat Sep 26 06:48:22 UTC 2026
% 0.07/5.37 % CPUTime :
% 0.07/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.03/7.74 % SZS status Unsatisfiable for theBenchmark.p
% 16.03/7.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------