%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET011-1 : 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 : n020.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 20.63s 3.07s
% Output : CNFRefutation 20.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 38 ( 10 unt; 19 nHn; 27 RR)
% Number of literals : 98 ( 0 equ; 34 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 62 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a_minus_b,hypothesis,
difference(a,b,aDb) ).
cnf(a_minus_aDb,hypothesis,
difference(a,aDb,'aD$uaDb') ).
cnf(prove_a_intersection_b_is_aD_aDb,negated_conjecture,
~ intersection(a,b,'aD$uaDb') ).
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(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,
difference(a,b,aDb),
inference(clausification,[status(esa)],[a_minus_b]) ).
cnf(c1,plain,
difference(a,aDb,'aD$uaDb'),
inference(clausification,[status(esa)],[a_minus_aDb]) ).
cnf(c2,plain,
~ intersection(a,b,'aD$uaDb'),
inference(clausification,[status(esa)],[prove_a_intersection_b_is_aD_aDb]) ).
cnf(c12,plain,
( member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(clausification,[status(esa)],[intersection_axiom1]) ).
cnf(c13,plain,
( member(h(X0,X1,X2),X1)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X2) ),
inference(clausification,[status(esa)],[intersection_axiom2]) ).
cnf(c14,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(c15,plain,
( member(X3,X0)
| ~ member(X3,X2)
| ~ difference(X0,X1,X2) ),
inference(clausification,[status(esa)],[member_of_difference]) ).
cnf(c16,plain,
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[not_member_of_difference]) ).
cnf(c17,plain,
( member(X0,X2)
| member(X0,X3)
| ~ difference(X1,X2,X3)
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[member_of_difference_or_set2]) ).
cnf(d0,plain,
( ~ member(X0,aDb)
| ~ member(X0,'aD$uaDb') ),
inference(resolution,[status(thm)],[c16,c1]) ).
cnf(d1,plain,
( member(h(X0,X1,'aD$uaDb'),X1)
| intersection(X0,X1,'aD$uaDb')
| ~ member(h(X0,X1,'aD$uaDb'),aDb) ),
inference(resolution,[status(thm)],[d0,c13]) ).
cnf(d2,plain,
( ~ member(X0,'aD$uaDb')
| member(X0,a) ),
inference(resolution,[status(thm)],[c15,c1]) ).
cnf(d3,plain,
( member(h(X0,X1,'aD$uaDb'),a)
| member(h(X0,X1,'aD$uaDb'),X1)
| intersection(X0,X1,'aD$uaDb') ),
inference(resolution,[status(thm)],[c13,d2]) ).
cnf(d4,plain,
( ~ member(X0,a)
| member(X0,b)
| member(X0,aDb) ),
inference(resolution,[status(thm)],[c17,c0]) ).
cnf(d5,plain,
( member(h(X0,X1,'aD$uaDb'),X1)
| intersection(X0,X1,'aD$uaDb')
| member(h(X0,X1,'aD$uaDb'),aDb)
| member(h(X0,X1,'aD$uaDb'),b) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( member(h(X0,X1,'aD$uaDb'),X1)
| intersection(X0,X1,'aD$uaDb')
| member(h(X0,X1,'aD$uaDb'),b)
| member(h(X0,X1,'aD$uaDb'),X1)
| intersection(X0,X1,'aD$uaDb') ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( member(h(X0,b,'aD$uaDb'),b)
| intersection(X0,b,'aD$uaDb') ),
inference(factoring,[status(thm)],[d6]) ).
cnf(d8,plain,
( ~ member(X0,b)
| ~ member(X0,aDb) ),
inference(resolution,[status(thm)],[c16,c0]) ).
cnf(d9,plain,
( member(h(X0,X1,'aD$uaDb'),X0)
| intersection(X0,X1,'aD$uaDb')
| member(h(X0,X1,'aD$uaDb'),a) ),
inference(resolution,[status(thm)],[d2,c12]) ).
cnf(d10,plain,
( member(h(a,X0,'aD$uaDb'),a)
| intersection(a,X0,'aD$uaDb') ),
inference(factoring,[status(thm)],[d9]) ).
cnf(d11,plain,
( ~ member(h(a,X0,'aD$uaDb'),X0)
| ~ member(h(a,X0,'aD$uaDb'),'aD$uaDb')
| intersection(a,X0,'aD$uaDb')
| intersection(a,X0,'aD$uaDb') ),
inference(resolution,[status(thm)],[d10,c14]) ).
cnf(d12,plain,
( ~ member(X0,a)
| member(X0,aDb)
| member(X0,'aD$uaDb') ),
inference(resolution,[status(thm)],[c17,c1]) ).
cnf(d13,plain,
( member(h(a,X0,'aD$uaDb'),'aD$uaDb')
| member(h(a,X0,'aD$uaDb'),aDb)
| intersection(a,X0,'aD$uaDb') ),
inference(resolution,[status(thm)],[d10,d12]) ).
cnf(d14,plain,
( ~ member(h(a,X0,'aD$uaDb'),X0)
| intersection(a,X0,'aD$uaDb')
| member(h(a,X0,'aD$uaDb'),aDb)
| intersection(a,X0,'aD$uaDb') ),
inference(resolution,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
( intersection(a,b,'aD$uaDb')
| member(h(a,b,'aD$uaDb'),aDb)
| intersection(a,b,'aD$uaDb') ),
inference(resolution,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
member(h(a,b,'aD$uaDb'),aDb),
inference(resolution,[status(thm)],[c2,d15]) ).
cnf(d17,plain,
~ member(h(a,b,'aD$uaDb'),b),
inference(resolution,[status(thm)],[d16,d8]) ).
cnf(d18,plain,
intersection(a,b,'aD$uaDb'),
inference(resolution,[status(thm)],[d17,d7]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[c2,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 06:50:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.63/3.07 % SZS status Unsatisfiable for theBenchmark.p
% 20.63/3.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------