%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET691+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 : n003.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 08:33:06 AM UTC 2026
% Result : Theorem 9.59s 1.69s
% Output : CNFRefutation 9.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 10 ~; 8 |; 1 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(equal_set,axiom,
! [X0,X1] :
( 'equal$uset'(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(empty_set,axiom,
! [X0] : ~ member(X0,'empty$uset') ).
fof(thI16,conjecture,
! [X0] :
( subset(X0,'empty$uset')
<=> 'equal$uset'(X0,'empty$uset') ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( subset(X0,'empty$uset')
<=> 'equal$uset'(X0,'empty$uset') ),
inference(negate_conjecture,[status(cth)],[thI16]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c3,plain,
( subset(X0,X1)
| ~ 'equal$uset'(X0,X1) ),
inference(clausification,[status(esa)],[equal_set]) ).
cnf(c5,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| 'equal$uset'(X0,X1) ),
inference(clausification,[status(esa)],[equal_set]) ).
cnf(c14,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set]) ).
cnf(c30,plain,
( 'equal$uset'(sK31,'empty$uset')
| subset(sK31,'empty$uset') ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c31,plain,
( ~ subset(sK31,'empty$uset')
| ~ 'equal$uset'(sK31,'empty$uset') ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( subset(sK31,'empty$uset')
| subset(sK31,'empty$uset') ),
inference(resolution,[status(thm)],[c3,c30]) ).
cnf(d1,plain,
( 'equal$uset'(sK31,'empty$uset')
| ~ subset('empty$uset',sK31) ),
inference(resolution,[status(thm)],[c5,d0]) ).
cnf(d2,plain,
subset('empty$uset',X0),
inference(resolution,[status(thm)],[c14,c1]) ).
cnf(d3,plain,
'equal$uset'(sK31,'empty$uset'),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
~ 'equal$uset'(sK31,'empty$uset'),
inference(resolution,[status(thm)],[d0,c31]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET691+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
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 08:08:08 UTC 2026
% 0.02/0.36 % CPUTime :
% 0.02/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.59/1.69 % SZS status Theorem for theBenchmark.p
% 9.59/1.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------