%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET591+3 : 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 : n017.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 08:32:50 AM UTC 2026
% Result : Theorem 11.38s 1.85s
% Output : CNFRefutation 11.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% Number of atoms : 53 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 22 ~; 17 |; 2 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 6 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(difference_defn,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ) ).
fof(empty_set_defn,axiom,
! [X0] : ~ member(X0,'empty$uset') ).
fof(equal_defn,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(empty_defn,axiom,
! [X0] :
( empty(X0)
<=> ! [X1] : ~ member(X1,X0) ) ).
fof(prove_th50,conjecture,
! [X0,X1] :
( subset(X0,difference(X1,X0))
=> X0 = 'empty$uset' ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( subset(X0,difference(X1,X0))
=> X0 = 'empty$uset' ),
inference(negate_conjecture,[status(cth)],[prove_th50]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c4,plain,
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c6,plain,
~ member(X0,'empty$uset'),
inference(clausification,[status(esa)],[empty_set_defn]) ).
cnf(c9,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_defn]) ).
cnf(c11,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c12,plain,
( member(sK13(X0),X0)
| empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c13,plain,
subset(sK14,difference(sK15,sK14)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c14,plain,
sK14 != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( subset(X0,X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[c11,c1]) ).
cnf(d1,plain,
subset('empty$uset',X0),
inference(resolution,[status(thm)],[c6,c1]) ).
cnf(d2,plain,
( ~ subset(X0,'empty$uset')
| 'empty$uset' = X0 ),
inference(resolution,[status(thm)],[c9,d1]) ).
cnf(d3,plain,
( ~ empty(X0)
| 'empty$uset' = X0 ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( member(sK13(X0),X1)
| ~ subset(X0,X1)
| empty(X0) ),
inference(resolution,[status(thm)],[c12,c0]) ).
cnf(d5,plain,
( ~ member(sK13(X0),X2)
| empty(X0)
| ~ subset(X0,difference(X1,X2)) ),
inference(resolution,[status(thm)],[d4,c4]) ).
cnf(d6,plain,
( empty(sK14)
| ~ member(sK13(sK14),sK14) ),
inference(resolution,[status(thm)],[d5,c13]) ).
cnf(d7,plain,
( empty(sK14)
| empty(sK14) ),
inference(resolution,[status(thm)],[d6,c12]) ).
cnf(d8,plain,
'empty$uset' = sK14,
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
sK14 != sK14,
inference(demodulation,[status(thm)],[c14,d8]) ).
cnf(d10,plain,
$false,
inference(equality_resolution,[status(thm)],[d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET591+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n017.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sat Sep 26 07:53:20 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.38/1.85 % SZS status Theorem for theBenchmark.p
% 11.38/1.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------