%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET620+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 : n008.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 15.04s 2.23s
% Output : CNFRefutation 15.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 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 : 31 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [X0,X1] : 'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)) ).
fof(difference_into_intersection,axiom,
! [X0,X1] : difference(X0,intersection(X0,X1)) = difference(X0,X1) ).
fof(difference_distributes_over_union,axiom,
! [X0,X1,X2] : difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)) ).
fof(commutativity_of_intersection,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0) ).
fof(prove_th96,conjecture,
! [X0,X1] : 'symmetric$udifference'(X0,X1) = difference(union(X0,X1),intersection(X0,X1)) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] : 'symmetric$udifference'(X0,X1) = difference(union(X0,X1),intersection(X0,X1)),
inference(negate_conjecture,[status(cth)],[prove_th96]) ).
cnf(c0,plain,
'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(clausification,[status(esa)],[symmetric_difference_defn]) ).
cnf(c1,plain,
difference(X0,intersection(X0,X1)) = difference(X0,X1),
inference(clausification,[status(esa)],[difference_into_intersection]) ).
cnf(c2,plain,
difference(union(X0,X1),X2) = union(difference(X0,X2),difference(X1,X2)),
inference(clausification,[status(esa)],[difference_distributes_over_union]) ).
cnf(c16,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_intersection]) ).
cnf(c28,plain,
'symmetric$udifference'(sK33,sK34) != difference(union(sK33,sK34),intersection(sK33,sK34)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
difference(union(X0,X2),intersection(X0,X1)) = union(difference(X0,X1),difference(X2,intersection(X0,X1))),
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
difference(X0,intersection(X1,X0)) = difference(X0,X1),
inference(superposition,[status(thm)],[c16,c1]) ).
cnf(d2,plain,
difference(union(X1,X0),intersection(X1,X0)) = union(difference(X1,X0),difference(X0,X1)),
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
difference(union(X0,X1),intersection(X0,X1)) = 'symmetric$udifference'(X0,X1),
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
'symmetric$udifference'(sK33,sK34) != 'symmetric$udifference'(sK33,sK34),
inference(demodulation,[status(thm)],[c28,d3]) ).
cnf(d5,plain,
$false,
inference(equality_resolution,[status(thm)],[d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET620+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
% 0.09/0.36 % Computer : n008.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 08:01:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.04/2.23 % SZS status Theorem for theBenchmark.p
% 15.04/2.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------