%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET626+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 08:32:56 AM UTC 2026
% Result : Theorem 10.34s 1.77s
% Output : CNFRefutation 10.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 5 unt; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 31 ( 13 ~; 11 |; 2 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 1 sgn 13 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ) ).
fof(intersect_defn,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ) ).
fof(symmetry_of_intersect,axiom,
! [X0,X1] :
( intersect(X0,X1)
=> intersect(X1,X0) ) ).
fof(prove_th102,conjecture,
! [X0,X1,X2] :
( intersect(X0,intersection(X1,X2))
=> intersect(X0,X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( intersect(X0,intersection(X1,X2))
=> intersect(X0,X1) ),
inference(negate_conjecture,[status(cth)],[prove_th102]) ).
cnf(c0,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c3,plain,
( member(sK5(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c4,plain,
( member(sK5(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c5,plain,
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(clausification,[status(esa)],[intersect_defn]) ).
cnf(c7,plain,
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(clausification,[status(esa)],[symmetry_of_intersect]) ).
cnf(c14,plain,
intersect(sK15,intersection(sK16,sK17)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
~ intersect(sK15,sK16),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
intersect(intersection(sK16,sK17),sK15),
inference(resolution,[status(thm)],[c7,c14]) ).
cnf(d1,plain,
( member(sK5(intersection(X0,X1),X2),X0)
| ~ intersect(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[c3,c0]) ).
cnf(d2,plain,
( ~ intersect(X0,X1)
| intersect(X1,X2)
| ~ member(sK5(X0,X1),X2) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(d3,plain,
( ~ intersect(intersection(X1,X2),X0)
| ~ intersect(intersection(X1,X2),X0)
| intersect(X0,X1) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
intersect(sK15,sK16),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[c15,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET626+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.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 08:02:10 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.34/1.77 % SZS status Theorem for theBenchmark.p
% 10.34/1.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------