%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET638+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 : n014.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 19.30s 2.99s
% Output : CNFRefutation 19.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 18 unt; 0 def)
% Number of atoms : 28 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 9 ( 3 ~; 1 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(intersection_is_subset,axiom,
! [X0,X1] : subset(intersection(X0,X1),X0) ).
fof(subset_intersection,axiom,
! [X0,X1] :
( subset(X0,X1)
=> intersection(X0,X1) = X0 ) ).
fof(union_empty_set,axiom,
! [X0] : union(X0,'empty$uset') = X0 ).
fof(intersection_distributes_over_union,axiom,
! [X0,X1,X2] : intersection(X0,union(X1,X2)) = union(intersection(X0,X1),intersection(X0,X2)) ).
fof(commutativity_of_intersection,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0) ).
fof(prove_th120,conjecture,
! [X0,X1,X2] :
( ( intersection(X0,X2) = 'empty$uset'
& subset(X0,union(X1,X2)) )
=> subset(X0,X1) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( intersection(X0,X2) = 'empty$uset'
& subset(X0,union(X1,X2)) )
=> subset(X0,X1) ),
inference(negate_conjecture,[status(cth)],[prove_th120]) ).
cnf(c0,plain,
subset(intersection(X0,X1),X0),
inference(clausification,[status(esa)],[intersection_is_subset]) ).
cnf(c1,plain,
( intersection(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_intersection]) ).
cnf(c2,plain,
union(X0,'empty$uset') = X0,
inference(clausification,[status(esa)],[union_empty_set]) ).
cnf(c3,plain,
intersection(X0,union(X1,X2)) = union(intersection(X0,X1),intersection(X0,X2)),
inference(clausification,[status(esa)],[intersection_distributes_over_union]) ).
cnf(c18,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_intersection]) ).
cnf(c28,plain,
subset(sK33,union(sK34,sK35)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c29,plain,
intersection(sK33,sK35) = 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c30,plain,
~ subset(sK33,sK34),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
subset(intersection(X1,X0),X0),
inference(superposition,[status(thm)],[c18,c0]) ).
cnf(d1,plain,
intersection(sK33,union(X0,sK35)) = union(intersection(sK33,X0),'empty$uset'),
inference(superposition,[status(thm)],[c29,c3]) ).
cnf(d2,plain,
intersection(sK33,union(X0,sK35)) = intersection(sK33,X0),
inference(demodulation,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
intersection(sK33,union(sK34,sK35)) = sK33,
inference(resolution,[status(thm)],[c1,c28]) ).
cnf(d4,plain,
intersection(sK33,sK34) = sK33,
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
subset(sK33,sK34),
inference(superposition,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c30,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET638+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n014.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 08:02:02 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.30/2.99 % SZS status Theorem for theBenchmark.p
% 19.30/2.99 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------