%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET008+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 : n001.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 08:31:31 AM UTC 2026
% Result : Theorem 17.51s 7.59s
% Output : CNFRefutation 17.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 15 unt; 0 def)
% Number of atoms : 84 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 25 ~; 28 |; 3 &)
% ( 7 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 11 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_defn,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ) ).
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$uset') ).
fof(equal_defn,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ).
fof(commutativity_of_intersection,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0) ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(empty_defn,axiom,
! [X0] :
( empty(X0)
<=> ! [X1] : ~ member(X1,X0) ) ).
fof(equal_member_defn,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ) ).
fof(prove_intersection_difference_empty_set,conjecture,
! [X0,X1] : intersection(difference(X0,X1),X1) = 'empty$uset' ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : intersection(difference(X0,X1),X1) = 'empty$uset',
inference(negate_conjecture,[status(cth)],[prove_intersection_difference_empty_set]) ).
cnf(c0,plain,
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c1,plain,
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(clausification,[status(esa)],[intersection_defn]) ).
cnf(c3,plain,
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c4,plain,
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c6,plain,
~ member(X0,'empty$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(c10,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_intersection]) ).
cnf(c12,plain,
( member(sK14(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c15,plain,
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c16,plain,
( member(sK18(X0),X0)
| empty(X0) ),
inference(clausification,[status(esa)],[empty_defn]) ).
cnf(c20,plain,
( member(sK22(X0,X1),X1)
| member(sK22(X0,X1),X0)
| X0 = X1 ),
inference(clausification,[status(esa)],[equal_member_defn]) ).
cnf(c23,plain,
intersection(difference(sK23,sK24),sK24) != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
subset('empty$uset',X0),
inference(resolution,[status(thm)],[c12,c6]) ).
cnf(d1,plain,
( ~ empty(X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[c12,c15]) ).
cnf(d2,plain,
( ~ subset(X1,X0)
| X1 = X0
| ~ empty(X0) ),
inference(resolution,[status(thm)],[d1,c9]) ).
cnf(d3,plain,
( ~ empty(X0)
| 'empty$uset' = X0 ),
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
( member(sK18(intersection(X0,X1)),X0)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[c16,c0]) ).
cnf(d5,plain,
( member(sK18(intersection(X0,X1)),X1)
| empty(intersection(X0,X1)) ),
inference(resolution,[status(thm)],[c16,c1]) ).
cnf(d6,plain,
( ~ member(sK18(intersection(X0,difference(X1,X2))),X2)
| empty(intersection(X0,difference(X1,X2))) ),
inference(resolution,[status(thm)],[d5,c4]) ).
cnf(d7,plain,
( empty(intersection(X0,difference(X1,X0)))
| empty(intersection(X0,difference(X1,X0))) ),
inference(resolution,[status(thm)],[d6,d4]) ).
cnf(d8,plain,
'empty$uset' = intersection(X0,difference(X1,X0)),
inference(resolution,[status(thm)],[d7,d3]) ).
cnf(d9,plain,
intersection(sK24,difference(sK23,sK24)) != 'empty$uset',
inference(demodulation,[status(thm)],[c23,c10]) ).
cnf(d10,plain,
'empty$uset' != 'empty$uset',
inference(demodulation,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( ~ subset(X0,'empty$uset')
| X0 = 'empty$uset' ),
inference(resolution,[status(thm)],[d0,c9]) ).
cnf(d12,plain,
( ~ empty(X0)
| X0 = 'empty$uset' ),
inference(resolution,[status(thm)],[d11,d1]) ).
cnf(d13,plain,
( member(sK18(difference(X0,X1)),X0)
| empty(difference(X0,X1)) ),
inference(resolution,[status(thm)],[c16,c3]) ).
cnf(d14,plain,
empty(difference('empty$uset',X0)),
inference(resolution,[status(thm)],[d13,c6]) ).
cnf(d15,plain,
difference('empty$uset',X0) = 'empty$uset',
inference(resolution,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
( member(sK22(X0,difference(X1,X2)),X1)
| member(sK22(X0,difference(X1,X2)),X0)
| X0 = difference(X1,X2) ),
inference(resolution,[status(thm)],[c20,c3]) ).
cnf(d17,plain,
( member(sK22(X0,difference(X0,X1)),X0)
| X0 = difference(X0,X1) ),
inference(factoring,[status(thm)],[d16]) ).
cnf(d18,plain,
( member(sK22('empty$uset',X0),X0)
| 'empty$uset' = X0 ),
inference(resolution,[status(thm)],[c20,c6]) ).
cnf(d19,plain,
( ~ member(sK22('empty$uset',difference(X0,X1)),X1)
| 'empty$uset' = difference(X0,X1) ),
inference(resolution,[status(thm)],[d18,c4]) ).
cnf(d20,plain,
( 'empty$uset' = difference('empty$uset','empty$uset')
| 'empty$uset' = difference('empty$uset','empty$uset') ),
inference(resolution,[status(thm)],[d19,d17]) ).
cnf(d21,plain,
'empty$uset' = 'empty$uset',
inference(demodulation,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[d21,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET008+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
% 0.09/5.37 % Computer : n001.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 06:54:34 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.51/7.59 % SZS status Theorem for theBenchmark.p
% 17.51/7.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------