%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET633+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 : 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 08:32:58 AM UTC 2026
% Result : Theorem 10.92s 1.78s
% Output : CNFRefutation 10.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 7 unt; 0 def)
% Number of atoms : 24 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 7 ~; 5 |; 3 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(symmetric_difference_defn,axiom,
! [X0,X1] : 'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)) ).
fof(union_subset,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(union(X0,X2),X1) ) ).
fof(prove_th115,conjecture,
! [X0,X1,X2] :
( ( subset(difference(X1,X0),X2)
& subset(difference(X0,X1),X2) )
=> subset('symmetric$udifference'(X0,X1),X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( ( subset(difference(X1,X0),X2)
& subset(difference(X0,X1),X2) )
=> subset('symmetric$udifference'(X0,X1),X2) ),
inference(negate_conjecture,[status(cth)],[prove_th115]) ).
cnf(c0,plain,
'symmetric$udifference'(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(clausification,[status(esa)],[symmetric_difference_defn]) ).
cnf(c1,plain,
( subset(union(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[union_subset]) ).
cnf(c17,plain,
subset(difference(sK21,sK22),sK23),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c18,plain,
subset(difference(sK22,sK21),sK23),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c19,plain,
~ subset('symmetric$udifference'(sK21,sK22),sK23),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ subset(difference(X1,X0),X2)
| ~ subset(difference(X0,X1),X2)
| subset('symmetric$udifference'(X0,X1),X2) ),
inference(superposition,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
( ~ subset(difference(sK22,sK21),sK23)
| subset('symmetric$udifference'(sK21,sK22),sK23) ),
inference(resolution,[status(thm)],[d0,c17]) ).
cnf(d2,plain,
subset('symmetric$udifference'(sK21,sK22),sK23),
inference(resolution,[status(thm)],[c18,d1]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[c19,d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET633+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
% 0.09/0.35 % 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 08:04:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.92/1.78 % SZS status Theorem for theBenchmark.p
% 10.92/1.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------