%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET355+4 : 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 : n012.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 08:32:31 AM UTC 2026
% Result : Theorem 12.62s 1.97s
% Output : CNFRefutation 12.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 25 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 6 ~; 5 |; 1 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 9 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(subset,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ) ).
fof(sum,axiom,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ) ).
fof(thI43,conjecture,
! [X0,X1] :
( member(X1,X0)
=> subset(X1,sum(X0)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0,X1] :
( member(X1,X0)
=> subset(X1,sum(X0)) ),
inference(negate_conjecture,[status(cth)],[thI43]) ).
cnf(c1,plain,
( member(sK3(X0,X1),X0)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c2,plain,
( ~ member(sK3(X0,X1),X1)
| subset(X0,X1) ),
inference(clausification,[status(esa)],[subset]) ).
cnf(c25,plain,
( ~ member(X0,X2)
| ~ member(X2,X1)
| member(X0,sum(X1)) ),
inference(clausification,[status(esa)],[sum]) ).
cnf(c29,plain,
member(sK32,sK31),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c30,plain,
~ subset(sK32,sum(sK31)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
member(sK3(sK32,sum(sK31)),sK32),
inference(resolution,[status(thm)],[c1,c30]) ).
cnf(d1,plain,
( member(X0,sum(sK31))
| ~ member(X0,sK32) ),
inference(resolution,[status(thm)],[c25,c29]) ).
cnf(d2,plain,
member(sK3(sK32,sum(sK31)),sum(sK31)),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
subset(sK32,sum(sK31)),
inference(resolution,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
$false,
inference(resolution,[status(thm)],[c30,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET355+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Sat Sep 26 07:34:19 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.62/1.97 % SZS status Theorem for theBenchmark.p
% 12.62/1.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------