%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET063+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 08:31:50 AM UTC 2026
% Result : Theorem 10.45s 3.02s
% Output : CNFRefutation 10.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 7 unt; 0 def)
% Number of atoms : 19 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 6 ~; 3 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 8 ( 1 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_subset,axiom,
! [X0] : subset('empty$uset',X0) ).
fof(equal_defn,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(prove_subset_of_empty_set_is_empty_set,conjecture,
! [X0] :
( subset(X0,'empty$uset')
=> X0 = 'empty$uset' ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( subset(X0,'empty$uset')
=> X0 = 'empty$uset' ),
inference(negate_conjecture,[status(cth)],[prove_subset_of_empty_set_is_empty_set]) ).
cnf(c0,plain,
subset('empty$uset',X0),
inference(clausification,[status(esa)],[empty_set_subset]) ).
cnf(c7,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_defn]) ).
cnf(c11,plain,
subset(sK12,'empty$uset'),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c12,plain,
sK12 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ subset('empty$uset',sK12)
| 'empty$uset' = sK12 ),
inference(resolution,[status(thm)],[c7,c11]) ).
cnf(d1,plain,
'empty$uset' = sK12,
inference(resolution,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
'empty$uset' != 'empty$uset',
inference(demodulation,[status(thm)],[c12,d1]) ).
cnf(d3,plain,
$false,
inference(equality_resolution,[status(thm)],[d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET063+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n013.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 07:00:53 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.45/3.02 % SZS status Theorem for theBenchmark.p
% 10.45/3.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------