%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET063+4 : 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 : n013.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 08:31:50 AM UTC 2026
% Result : Theorem 12.94s 3.74s
% Output : CNFRefutation 12.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 18 ( 8 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 9 ~; 8 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 4 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(equal_set,axiom,
! [X0,X1] :
( 'equal$uset'(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(intersection,axiom,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
<=> ( member(X0,X2)
& member(X0,X1) ) ) ).
fof(empty_set,axiom,
! [X0] : ~ member(X0,'empty$uset') ).
fof(thI17,conjecture,
! [X0] : 'equal$uset'(intersection(X0,'empty$uset'),'empty$uset') ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : 'equal$uset'(intersection(X0,'empty$uset'),'empty$uset'),
inference(negate_conjecture,[status(cth)],[thI17]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c2,plain,
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| 'equal$uset'(X0,X1) ),
inference(clausification,[status(esa)],[equal_set]) ).
cnf(c9,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection]) ).
cnf(c14,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set]) ).
cnf(c29,plain,
~ 'equal$uset'(intersection(sK31,'empty$uset'),'empty$uset'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
subset('empty$uset',X0),
inference(resolution,[status(thm)],[c1,c14]) ).
cnf(d1,plain,
( subset(intersection(X0,X1),X2)
| member(sK3(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d2,plain,
( subset(intersection(X0,X1),X1)
| subset(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
( 'equal$uset'(intersection(X1,X0),X0)
| ~ subset(X0,intersection(X1,X0)) ),
inference(resolution,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
'equal$uset'(intersection(X0,'empty$uset'),'empty$uset'),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,c29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET063+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.55 % Computer : n013.cluster.edu
% 0.10/0.55 % Model : x86_64 x86_64
% 0.10/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.55 % Memory : 8046.5625MB
% 0.10/0.55 % OS : Linux 6.8.0-71-generic
% 0.10/0.55 % CPULimit : 300
% 0.10/0.55 % WCLimit : 300
% 0.10/0.55 % DateTime : Sat Sep 26 07:00:53 UTC 2026
% 0.10/0.55 % CPUTime :
% 0.10/0.55 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.94/3.74 % SZS status Theorem for theBenchmark.p
% 12.94/3.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------