%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET617+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 : n017.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 10.40s 1.75s
% Output : CNFRefutation 10.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 17 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 2 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 24 ( 1 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [X0,X1] : 'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)) ).
fof(union_empty_set,axiom,
! [X0] : union(X0,'empty$uset') = X0 ).
fof(no_difference_with_empty_set1,axiom,
! [X0] : difference(X0,'empty$uset') = X0 ).
fof(no_difference_with_empty_set2,axiom,
! [X0] : difference('empty$uset',X0) = 'empty$uset' ).
fof(commutativity_of_union,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0) ).
fof(commutativity_of_symmetric_difference,axiom,
! [X0,X1] : 'symmetric$udifference'(X0,X1) = 'symmetric$udifference'(X1,X0) ).
fof(prove_th92,conjecture,
! [X0] :
( 'symmetric$udifference'('empty$uset',X0) = X0
& 'symmetric$udifference'(X0,'empty$uset') = X0 ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( 'symmetric$udifference'('empty$uset',X0) = X0
& 'symmetric$udifference'(X0,'empty$uset') = X0 ),
inference(negate_conjecture,[status(cth)],[prove_th92]) ).
cnf(c0,plain,
'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(clausification,[status(esa)],[symmetric_difference_defn]) ).
cnf(c1,plain,
union(X0,'empty$uset') = X0,
inference(clausification,[status(esa)],[union_empty_set]) ).
cnf(c2,plain,
difference(X0,'empty$uset') = X0,
inference(clausification,[status(esa)],[no_difference_with_empty_set1]) ).
cnf(c3,plain,
difference('empty$uset',X0) = 'empty$uset',
inference(clausification,[status(esa)],[no_difference_with_empty_set2]) ).
cnf(c8,plain,
union(X0,X1) = union(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_union]) ).
cnf(c9,plain,
'symmetric$udifference'(X0,X1) = 'symmetric$udifference'(X1,X0),
inference(clausification,[status(esa)],[commutativity_of_symmetric_difference]) ).
cnf(c22,plain,
( 'symmetric$udifference'('empty$uset',sK24) != sK24
| 'symmetric$udifference'(sK24,'empty$uset') != sK24 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( 'symmetric$udifference'('empty$uset',sK24) != sK24
| 'symmetric$udifference'('empty$uset',sK24) != sK24 ),
inference(demodulation,[status(thm)],[c22,c9]) ).
cnf(d1,plain,
'symmetric$udifference'('empty$uset',X0) = union(difference('empty$uset',X0),X0),
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d2,plain,
'symmetric$udifference'('empty$uset',X0) = union(X0,difference('empty$uset',X0)),
inference(demodulation,[status(thm)],[d1,c8]) ).
cnf(d3,plain,
'symmetric$udifference'('empty$uset',X0) = union(X0,'empty$uset'),
inference(demodulation,[status(thm)],[d2,c3]) ).
cnf(d4,plain,
'symmetric$udifference'('empty$uset',X0) = X0,
inference(demodulation,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
$false,
inference(resolution,[status(thm)],[d4,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET617+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
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 07:56:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.40/1.75 % SZS status Theorem for theBenchmark.p
% 10.40/1.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------