%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET062+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 : n026.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 08:31:49 AM UTC 2026
% Result : Theorem 9.86s 7.67s
% Output : CNFRefutation 9.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 7 unt; 0 def)
% Number of atoms : 12 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 1 |; 0 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 2 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(empty_set_defn,axiom,
! [X0] : ~ member(X0,'empty$uset') ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(prove_empty_set_subset,conjecture,
! [X0] : subset('empty$uset',X0) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : subset('empty$uset',X0),
inference(negate_conjecture,[status(cth)],[prove_empty_set_subset]) ).
cnf(c0,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set_defn]) ).
cnf(c2,plain,
( member(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c7,plain,
~ subset('empty$uset',sK9),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
subset('empty$uset',X0),
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
$false,
inference(resolution,[status(thm)],[d0,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET062+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.43 % Computer : n026.cluster.edu
% 0.16/5.43 % Model : x86_64 x86_64
% 0.16/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.43 % Memory : 8046.5625MB
% 0.16/5.43 % OS : Linux 6.8.0-71-generic
% 0.16/5.43 % CPULimit : 300
% 0.16/5.43 % WCLimit : 300
% 0.16/5.43 % DateTime : Sat Sep 26 07:04:01 UTC 2026
% 0.16/5.43 % CPUTime :
% 0.16/5.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.86/7.67 % SZS status Theorem for theBenchmark.p
% 9.86/7.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------