%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET604+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 : 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 08:32:52 AM UTC 2026
% Result : Theorem 10.12s 1.63s
% Output : CNFRefutation 10.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 7 unt; 0 def)
% Number of atoms : 11 ( 6 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 2 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_subset,axiom,
! [X0] : subset('empty$uset',X0) ).
fof(difference_empty_set,axiom,
! [X0,X1] :
( difference(X0,X1) = 'empty$uset'
<=> subset(X0,X1) ) ).
fof(prove_no_difference_with_empty_set,conjecture,
! [X0] : difference('empty$uset',X0) = 'empty$uset' ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : difference('empty$uset',X0) = 'empty$uset',
inference(negate_conjecture,[status(cth)],[prove_no_difference_with_empty_set]) ).
cnf(c0,plain,
subset('empty$uset',X0),
inference(clausification,[status(esa)],[empty_set_subset]) ).
cnf(c2,plain,
( ~ subset(X0,X1)
| difference(X0,X1) = 'empty$uset' ),
inference(clausification,[status(esa)],[difference_empty_set]) ).
cnf(c16,plain,
difference('empty$uset',sK17) != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
difference('empty$uset',X0) = 'empty$uset',
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
$false,
inference(resolution,[status(thm)],[d0,c16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET604+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
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 07:58:07 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.12/1.63 % SZS status Theorem for theBenchmark.p
% 10.12/1.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------