%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET635+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 08:32:58 AM UTC 2026
% Result : Theorem 12.81s 2.22s
% Output : CNFRefutation 12.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 24 unt; 0 def)
% Number of atoms : 28 ( 23 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 1 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 3 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_is_subset,axiom,
! [X0,X1] : subset(intersection(X0,X1),X0) ).
fof(difference_empty_set,axiom,
! [X0,X1] :
( difference(X0,X1) = 'empty$uset'
<=> subset(X0,X1) ) ).
fof(union_empty_set,axiom,
! [X0] : union(X0,'empty$uset') = X0 ).
fof(difference_and_intersection_and_union,axiom,
! [X0,X1,X2] : difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)) ).
fof(difference_and_intersection,axiom,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2) ).
fof(commutativity_of_union,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0) ).
fof(prove_th117,conjecture,
! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),intersection(X0,X2)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] : intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),intersection(X0,X2)),
inference(negate_conjecture,[status(cth)],[prove_th117]) ).
cnf(c0,plain,
subset(intersection(X0,X1),X0),
inference(clausification,[status(esa)],[intersection_is_subset]) ).
cnf(c2,plain,
( ~ subset(X0,X1)
| difference(X0,X1) = 'empty$uset' ),
inference(clausification,[status(esa)],[difference_empty_set]) ).
cnf(c3,plain,
union(X0,'empty$uset') = X0,
inference(clausification,[status(esa)],[union_empty_set]) ).
cnf(c4,plain,
difference(X0,intersection(X1,X2)) = union(difference(X0,X1),difference(X0,X2)),
inference(clausification,[status(esa)],[difference_and_intersection_and_union]) ).
cnf(c5,plain,
intersection(X0,difference(X1,X2)) = difference(intersection(X0,X1),X2),
inference(clausification,[status(esa)],[difference_and_intersection]) ).
cnf(c15,plain,
union(X0,X1) = union(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_union]) ).
cnf(c30,plain,
intersection(sK36,difference(sK37,sK38)) != difference(intersection(sK36,sK37),intersection(sK36,sK38)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
union('empty$uset',X0) = X0,
inference(superposition,[status(thm)],[c15,c3]) ).
cnf(d1,plain,
difference(intersection(X0,X1),intersection(X2,X3)) = union(intersection(X0,difference(X1,X2)),difference(intersection(X0,X1),X3)),
inference(superposition,[status(thm)],[c5,c4]) ).
cnf(d2,plain,
intersection(X0,difference(X1,intersection(X2,X3))) = union(intersection(X0,difference(X1,X2)),difference(intersection(X0,X1),X3)),
inference(demodulation,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
intersection(X0,difference(X1,intersection(X3,X2))) = union(intersection(X0,difference(X1,X3)),intersection(X0,difference(X1,X2))),
inference(demodulation,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
difference(intersection(X0,X1),X0) = 'empty$uset',
inference(resolution,[status(thm)],[c2,c0]) ).
cnf(d5,plain,
intersection(X0,difference(X1,X0)) = 'empty$uset',
inference(demodulation,[status(thm)],[d4,c5]) ).
cnf(d6,plain,
intersection(X0,difference(X1,intersection(X0,X2))) = union('empty$uset',intersection(X0,difference(X1,X2))),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
intersection(X0,difference(X1,intersection(X0,X2))) = intersection(X0,difference(X1,X2)),
inference(demodulation,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
intersection(sK36,difference(sK37,sK38)) != intersection(sK36,difference(sK37,intersection(sK36,sK38))),
inference(demodulation,[status(thm)],[c30,c5]) ).
cnf(d9,plain,
intersection(sK36,difference(sK37,sK38)) != intersection(sK36,difference(sK37,sK38)),
inference(demodulation,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
$false,
inference(equality_resolution,[status(thm)],[d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET635+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
% 0.09/0.36 % Computer : n026.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 08:04:41 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.81/2.22 % SZS status Theorem for theBenchmark.p
% 12.81/2.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------