%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET618+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 : n005.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 10.26s 1.66s
% Output : CNFRefutation 10.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [X0,X1] : 'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)) ).
fof(idempotency_of_union,axiom,
! [X0] : union(X0,X0) = X0 ).
fof(self_difference_is_empty_set,axiom,
! [X0] : difference(X0,X0) = 'empty$uset' ).
fof(prove_th93,conjecture,
! [X0] : 'symmetric$udifference'(X0,X0) = 'empty$uset' ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] : 'symmetric$udifference'(X0,X0) = 'empty$uset',
inference(negate_conjecture,[status(cth)],[prove_th93]) ).
cnf(c0,plain,
'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(clausification,[status(esa)],[symmetric_difference_defn]) ).
cnf(c1,plain,
union(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotency_of_union]) ).
cnf(c2,plain,
difference(X0,X0) = 'empty$uset',
inference(clausification,[status(esa)],[self_difference_is_empty_set]) ).
cnf(c21,plain,
'symmetric$udifference'(sK23,sK23) != 'empty$uset',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'symmetric$udifference'(X0,X0) = difference(X0,X0),
inference(superposition,[status(thm)],[c1,c0]) ).
cnf(d1,plain,
'symmetric$udifference'(X0,X0) = 'empty$uset',
inference(demodulation,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
$false,
inference(resolution,[status(thm)],[d1,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET618+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
% 0.06/0.34 % Computer : n005.cluster.edu
% 0.06/0.34 % Model : x86_64 x86_64
% 0.06/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.34 % Memory : 8046.5625MB
% 0.06/0.34 % OS : Linux 6.8.0-71-generic
% 0.06/0.34 % CPULimit : 300
% 0.06/0.34 % WCLimit : 300
% 0.06/0.34 % DateTime : Sat Sep 26 08:01:18 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.34 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.26/1.66 % SZS status Theorem for theBenchmark.p
% 10.26/1.66 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------