%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET009+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 : n020.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 08:31:32 AM UTC 2026
% Result : Theorem 9.82s 2.16s
% Output : CNFRefutation 9.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 3 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 36 ( 13 ~; 17 |; 1 &)
% ( 2 <=>; 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_subset_difference,conjecture,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X2,X1),difference(X2,X0)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1,X2] :
( subset(X0,X1)
=> subset(difference(X2,X1),difference(X2,X0)) ),
inference(negate_conjecture,[status(cth)],[prove_subset_difference]) ).
cnf(c0,plain,
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c1,plain,
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c2,plain,
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(clausification,[status(esa)],[difference_defn]) ).
cnf(c3,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c4,plain,
( member(sK6(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c5,plain,
( ~ member(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset_defn]) ).
cnf(c7,plain,
subset(sK8,sK9),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c8,plain,
~ subset(difference(sK10,sK9),difference(sK10,sK8)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ member(sK6(difference(X0,X1),X2),X1)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d1,plain,
( ~ member(X0,sK8)
| member(X0,sK9) ),
inference(resolution,[status(thm)],[c3,c7]) ).
cnf(d2,plain,
( member(sK6(difference(X0,X1),X2),X0)
| subset(difference(X0,X1),X2) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d3,plain,
( ~ member(sK6(X0,difference(X1,X2)),X1)
| member(sK6(X0,difference(X1,X2)),X2)
| subset(X0,difference(X1,X2)) ),
inference(resolution,[status(thm)],[c5,c2]) ).
cnf(d4,plain,
( subset(difference(X0,X1),difference(X0,X2))
| subset(difference(X0,X1),difference(X0,X2))
| member(sK6(difference(X0,X1),difference(X0,X2)),X2) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( member(sK6(difference(X0,X1),difference(X0,sK8)),sK9)
| subset(difference(X0,X1),difference(X0,sK8)) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( subset(difference(X0,sK9),difference(X0,sK8))
| subset(difference(X0,sK9),difference(X0,sK8)) ),
inference(resolution,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,c8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET009+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
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 06:49:48 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.82/2.16 % SZS status Theorem for theBenchmark.p
% 9.82/2.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------