%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET585+3 : TPTP v9.3.1. Released v2.2.0.
% 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 08:32:48 AM UTC 2026
% Result : Theorem 10.17s 1.68s
% Output : CNFRefutation 10.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 9 unt; 0 def)
% Number of atoms : 17 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 11 ( 6 ~; 3 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 3 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitivity_of_subset,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ).
fof(subset_of_union,axiom,
! [X0,X1] : subset(X0,union(X0,X1)) ).
fof(intersection_is_subset,axiom,
! [X0,X1] : subset(intersection(X0,X1),X0) ).
fof(prove_intersection_subset_of_union,conjecture,
! [X0,X1,X2] : subset(intersection(X0,X1),union(X0,X2)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] : subset(intersection(X0,X1),union(X0,X2)),
inference(negate_conjecture,[status(cth)],[prove_intersection_subset_of_union]) ).
cnf(c0,plain,
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_subset]) ).
cnf(c1,plain,
subset(X0,union(X0,X1)),
inference(clausification,[status(esa)],[subset_of_union]) ).
cnf(c2,plain,
subset(intersection(X0,X1),X0),
inference(clausification,[status(esa)],[intersection_is_subset]) ).
cnf(c21,plain,
~ subset(intersection(sK26,sK27),union(sK26,sK28)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ subset(X0,X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
~ subset(intersection(sK26,sK27),sK26),
inference(resolution,[status(thm)],[d0,c21]) ).
cnf(d2,plain,
$false,
inference(resolution,[status(thm)],[c2,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET585+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 07:57:32 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.17/1.68 % SZS status Theorem for theBenchmark.p
% 10.17/1.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------