%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET593+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 : n014.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 08:32:50 AM UTC 2026
% Result : Theorem 8.00s 4.06s
% Output : CNFRefutation 8.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 3 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 47 ( 15 ~; 23 |; 3 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 2 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union_defn,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ) ).
fof(difference_defn,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ) ).
fof(subset_defn,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(prove_th52,conjecture,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
=> ( subset(difference(X0,X2),X1)
& subset(difference(X0,X1),X2) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,union(X1,X2))
=> ( subset(difference(X0,X2),X1)
& subset(difference(X0,X1),X2) ) ),
inference(negate_conjecture,[status(cth)],[prove_th52]) ).
cnf(c0,plain,
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union_defn]) ).
cnf(c3,plain,
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c4,plain,
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c6,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c7,plain,
( member(sK9(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c8,plain,
( ~ member(sK9(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c17,plain,
subset(sK17,union(sK18,sK19)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c18,plain,
( ~ subset(difference(sK17,sK19),sK18)
| ~ subset(difference(sK17,sK18),sK19) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(sK9(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(d1,plain,
( ~ member(X0,sK17)
| member(X0,union(sK18,sK19)) ),
inference(resolution,[status(thm)],[c6,c17]) ).
cnf(d2,plain,
( member(X0,sK18)
| member(X0,sK19)
| ~ member(X0,sK17) ),
inference(resolution,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
( member(sK9(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(d4,plain,
( member(sK9(difference(sK17,X0),X1),sK19)
| member(sK9(difference(sK17,X0),X1),sK18)
| subset(difference(sK17,X0),X1) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( subset(difference(sK17,X0),sK19)
| subset(difference(sK17,X0),sK19)
| member(sK9(difference(sK17,X0),sK19),sK18) ),
inference(resolution,[status(thm)],[d4,c8]) ).
cnf(d6,plain,
( subset(difference(sK17,sK18),sK19)
| subset(difference(sK17,sK18),sK19) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
( subset(difference(sK17,sK19),X0)
| subset(difference(sK17,sK19),X0)
| member(sK9(difference(sK17,sK19),X0),sK18) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d8,plain,
( subset(difference(sK17,sK19),sK18)
| subset(difference(sK17,sK19),sK18) ),
inference(resolution,[status(thm)],[d7,c8]) ).
cnf(d9,plain,
~ subset(difference(sK17,sK18),sK19),
inference(resolution,[status(thm)],[d8,c18]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET593+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.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 07:58:01 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.00/4.06 % SZS status Theorem for theBenchmark.p
% 8.00/4.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------