%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET621+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 : n018.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 19.20s 2.88s
% Output : CNFRefutation 19.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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; 3 con; 0-2 aty)
% Number of variables : 31 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [X0,X1] : 'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)) ).
fof(difference_difference_union,axiom,
! [X0,X1,X2] : difference(difference(X0,X1),X2) = difference(X0,union(X1,X2)) ).
fof(difference_distributes_over_union,axiom,
! [X0,X1,X2] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)) ).
fof(prove_th97,conjecture,
! [X0,X1,X2] : difference('symmetric$udifference'(X0,X1),X2) = union(difference(X0,union(X1,X2)),difference(X1,union(X0,X2))) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] : difference('symmetric$udifference'(X0,X1),X2) = union(difference(X0,union(X1,X2)),difference(X1,union(X0,X2))),
inference(negate_conjecture,[status(cth)],[prove_th97]) ).
cnf(c0,plain,
'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(clausification,[status(esa)],[symmetric_difference_defn]) ).
cnf(c1,plain,
difference(difference(X0,X1),X2) = difference(X0,union(X1,X2)),
inference(clausification,[status(esa)],[difference_difference_union]) ).
cnf(c2,plain,
difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
inference(clausification,[status(esa)],[difference_distributes_over_union]) ).
cnf(c24,plain,
difference('symmetric$udifference'(sK29,sK30),sK31) != union(difference(sK29,union(sK30,sK31)),difference(sK30,union(sK29,sK31))),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
difference(union(difference(X0,X1),X3),X2) = union(difference(X0,union(X1,X2)),difference(X3,X2)),
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
difference(union(difference(X3,X4),difference(X0,X1)),X2) = union(difference(X3,union(X4,X2)),difference(X0,union(X1,X2))),
inference(superposition,[status(thm)],[c1,d0]) ).
cnf(d2,plain,
difference('symmetric$udifference'(sK29,sK30),sK31) != difference(union(difference(sK29,sK30),difference(sK30,sK29)),sK31),
inference(demodulation,[status(thm)],[c24,d1]) ).
cnf(d3,plain,
difference('symmetric$udifference'(sK29,sK30),sK31) != difference('symmetric$udifference'(sK29,sK30),sK31),
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
$false,
inference(equality_resolution,[status(thm)],[d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET621+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 08:03:21 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.20/2.88 % SZS status Theorem for theBenchmark.p
% 19.20/2.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------