%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET619+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 08:32:55 AM UTC 2026
% Result : Theorem 18.47s 2.64s
% Output : CNFRefutation 18.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 44 ( 2 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [X0,X1] : 'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)) ).
fof(associativity_of_union,axiom,
! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)) ).
fof(union_intersection,axiom,
! [X0,X1] : union(X0,intersection(X0,X1)) = X0 ).
fof(union_intersection_difference,axiom,
! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0 ).
fof(commutativity_of_union,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0) ).
fof(commutativity_of_intersection,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0) ).
fof(prove_th95,conjecture,
! [X0,X1] : union(X0,X1) = union('symmetric$udifference'(X0,X1),intersection(X0,X1)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : union(X0,X1) = union('symmetric$udifference'(X0,X1),intersection(X0,X1)),
inference(negate_conjecture,[status(cth)],[prove_th95]) ).
cnf(c0,plain,
'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(clausification,[status(esa)],[symmetric_difference_defn]) ).
cnf(c1,plain,
union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(clausification,[status(esa)],[associativity_of_union]) ).
cnf(c2,plain,
union(X0,intersection(X0,X1)) = X0,
inference(clausification,[status(esa)],[union_intersection]) ).
cnf(c3,plain,
union(intersection(X0,X1),difference(X0,X1)) = X0,
inference(clausification,[status(esa)],[union_intersection_difference]) ).
cnf(c13,plain,
union(X0,X1) = union(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_union]) ).
cnf(c14,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_intersection]) ).
cnf(c26,plain,
union(sK32,sK33) != union('symmetric$udifference'(sK32,sK33),intersection(sK32,sK33)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
union(sK32,sK33) != union(intersection(sK32,sK33),'symmetric$udifference'(sK32,sK33)),
inference(demodulation,[status(thm)],[c26,c13]) ).
cnf(d1,plain,
union(X0,X2) = union(X0,union(intersection(X0,X1),X2)),
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d2,plain,
union(intersection(X1,X0),difference(X0,X1)) = X0,
inference(superposition,[status(thm)],[c14,c3]) ).
cnf(d3,plain,
union(X0,difference(X1,X0)) = union(X0,X1),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
union(X0,X2) = union(intersection(X0,X1),union(difference(X0,X1),X2)),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d5,plain,
union(X0,difference(X1,X0)) = union(intersection(X0,X1),'symmetric$udifference'(X0,X1)),
inference(superposition,[status(thm)],[c0,d4]) ).
cnf(d6,plain,
union(X0,X1) = union(intersection(X0,X1),'symmetric$udifference'(X0,X1)),
inference(demodulation,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET619+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
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:03:55 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.47/2.64 % SZS status Theorem for theBenchmark.p
% 18.47/2.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------