%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET013-3 : 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 : n005.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 56.45s 9.31s
% Output : CNFRefutation 56.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 35 ( 12 unt; 6 nHn; 31 RR)
% Number of literals : 70 ( 15 equ; 26 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(intersection_of_a_and_b_is_c,hypothesis,
intersection(as,bs) = cs ).
cnf(intersection_of_b_and_a_is_d,hypothesis,
intersection(bs,as) = ds ).
cnf(prove_c_equals_d,negated_conjecture,
cs != ds ).
cnf(extensionality2,axiom,
( X0 = X1
| member(f1(X0,X1),X1)
| member(f1(X0,X1),X0) ) ).
cnf(extensionality3,axiom,
( X0 = X1
| ~ member(f1(X0,X1),X1)
| ~ member(f1(X0,X1),X0) ) ).
cnf(intersection1,axiom,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection2,axiom,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ) ).
cnf(intersection3,axiom,
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ) ).
cnf(c0,plain,
intersection(as,bs) = cs,
inference(clausification,[status(esa)],[intersection_of_a_and_b_is_c]) ).
cnf(c1,plain,
intersection(bs,as) = ds,
inference(clausification,[status(esa)],[intersection_of_b_and_a_is_d]) ).
cnf(c2,plain,
ds != cs,
inference(clausification,[status(esa)],[prove_c_equals_d]) ).
cnf(c5,plain,
( X1 = X0
| member(f1(X0,X1),X0)
| member(f1(X0,X1),X1) ),
inference(clausification,[status(esa)],[extensionality2]) ).
cnf(c6,plain,
( X1 = X0
| ~ member(f1(X0,X1),X0)
| ~ member(f1(X0,X1),X1) ),
inference(clausification,[status(esa)],[extensionality3]) ).
cnf(c30,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection1]) ).
cnf(c31,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection2]) ).
cnf(c32,plain,
( ~ member(X0,X2)
| member(X0,intersection(X1,X2))
| ~ member(X0,X1) ),
inference(clausification,[status(esa)],[intersection3]) ).
cnf(d0,plain,
( ~ member(X0,bs)
| ~ member(X0,as)
| member(X0,ds) ),
inference(superposition,[status(thm)],[c1,c32]) ).
cnf(d1,plain,
( member(X0,bs)
| ~ member(X0,cs) ),
inference(superposition,[status(thm)],[c0,c31]) ).
cnf(d2,plain,
( member(X0,bs)
| ~ member(X0,ds) ),
inference(superposition,[status(thm)],[c1,c30]) ).
cnf(d3,plain,
( member(f1(X0,ds),X0)
| ds = X0
| member(f1(X0,ds),bs) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
( member(f1(cs,ds),bs)
| member(f1(cs,ds),bs)
| ds = cs ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
member(f1(cs,ds),bs),
inference(resolution,[status(thm)],[c2,d4]) ).
cnf(d6,plain,
( member(f1(cs,ds),ds)
| ~ member(f1(cs,ds),as) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
( member(X0,as)
| ~ member(X0,ds) ),
inference(superposition,[status(thm)],[c1,c31]) ).
cnf(d8,plain,
( member(X0,as)
| ~ member(X0,cs) ),
inference(superposition,[status(thm)],[c0,c30]) ).
cnf(d9,plain,
( member(f1(cs,X0),X0)
| X0 = cs
| member(f1(cs,X0),as) ),
inference(resolution,[status(thm)],[d8,c5]) ).
cnf(d10,plain,
( member(f1(cs,ds),as)
| member(f1(cs,ds),as)
| ds = cs ),
inference(resolution,[status(thm)],[d9,d7]) ).
cnf(d11,plain,
member(f1(cs,ds),as),
inference(resolution,[status(thm)],[c2,d10]) ).
cnf(d12,plain,
member(f1(cs,ds),ds),
inference(resolution,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
( ~ member(X0,as)
| ~ member(X0,bs)
| member(X0,cs) ),
inference(superposition,[status(thm)],[c0,c32]) ).
cnf(d14,plain,
( member(f1(cs,ds),cs)
| ~ member(f1(cs,ds),as) ),
inference(resolution,[status(thm)],[d5,d13]) ).
cnf(d15,plain,
member(f1(cs,ds),cs),
inference(resolution,[status(thm)],[d11,d14]) ).
cnf(d16,plain,
( ~ member(f1(cs,ds),ds)
| ds = cs ),
inference(resolution,[status(thm)],[d15,c6]) ).
cnf(d17,plain,
~ member(f1(cs,ds),ds),
inference(resolution,[status(thm)],[c2,d16]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET013-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 06:49:16 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 56.45/9.31 % SZS status Unsatisfiable for theBenchmark.p
% 56.45/9.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------