%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET199+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 : 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 08:32:18 AM UTC 2026
% Result : Theorem 11.50s 2.08s
% Output : CNFRefutation 11.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 7 unt; 0 def)
% Number of atoms : 45 ( 2 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 35 ( 12 ~; 15 |; 3 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ) ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(commutativity_of_intersection,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0) ).
fof(prove_intersection_of_subsets,conjecture,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,intersection(X1,X2)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,intersection(X1,X2)) ),
inference(negate_conjecture,[status(cth)],[prove_intersection_of_subsets]) ).
cnf(c2,plain,
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c3,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c4,plain,
( member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c5,plain,
( ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c6,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_intersection]) ).
cnf(c14,plain,
subset(sK14,sK15),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c15,plain,
subset(sK14,sK16),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c16,plain,
~ subset(sK14,intersection(sK15,sK16)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(X0,sK14)
| member(X0,sK15) ),
inference(resolution,[status(thm)],[c3,c14]) ).
cnf(d1,plain,
( subset(sK14,X0)
| member(sK6(sK14,X0),sK15) ),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
( ~ member(X0,sK14)
| member(X0,sK16) ),
inference(resolution,[status(thm)],[c3,c15]) ).
cnf(d3,plain,
( member(sK6(sK14,X0),sK16)
| subset(sK14,X0) ),
inference(resolution,[status(thm)],[c4,d2]) ).
cnf(d4,plain,
( ~ member(sK6(X0,intersection(X1,X2)),X2)
| ~ member(sK6(X0,intersection(X1,X2)),X1)
| subset(X0,intersection(X1,X2)) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d5,plain,
( subset(sK14,intersection(sK16,X0))
| subset(sK14,intersection(sK16,X0))
| ~ member(sK6(sK14,intersection(sK16,X0)),X0) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( subset(sK14,intersection(sK16,sK15))
| subset(sK14,intersection(sK16,sK15)) ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
subset(sK14,intersection(sK15,sK16)),
inference(demodulation,[status(thm)],[d6,c6]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[c16,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET199+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.53 % Computer : n005.cluster.edu
% 0.11/0.53 % Model : x86_64 x86_64
% 0.11/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.53 % Memory : 8046.5625MB
% 0.11/0.53 % OS : Linux 6.8.0-71-generic
% 0.11/0.53 % CPULimit : 300
% 0.11/0.53 % WCLimit : 300
% 0.11/0.53 % DateTime : Sat Sep 26 07:19:02 UTC 2026
% 0.11/0.53 % CPUTime :
% 0.11/0.53 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.50/2.08 % SZS status Theorem for theBenchmark.p
% 11.50/2.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------