%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 08:33:16 AM UTC 2026
% Result : Theorem 28.38s 19.11s
% Output : CNFRefutation 28.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 4 unt; 0 def)
% Number of atoms : 23 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 6 ~; 5 |; 0 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(union,axiom,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
<=> ( member(X0,X2)
| member(X0,X1) ) ) ).
fof(singleton,axiom,
! [X0,X1] :
( member(X0,singleton(X1))
<=> X0 = X1 ) ).
fof(successor,axiom,
! [X0,X1] :
( member(X1,suc(X0))
<=> member(X1,union(X0,singleton(X0))) ) ).
fof(thV12,conjecture,
! [X0] :
( member(X0,on)
=> member(X0,suc(X0)) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( member(X0,on)
=> member(X0,suc(X0)) ),
inference(negate_conjecture,[status(cth)],[thV12]) ).
cnf(c13,plain,
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(clausification,[status(esa)],[union]) ).
cnf(c19,plain,
( X1 != X0
| member(X0,singleton(X1)) ),
inference(clausification,[status(esa)],[singleton]) ).
cnf(c63,plain,
( ~ member(X0,union(X1,singleton(X1)))
| member(X0,suc(X1)) ),
inference(clausification,[status(esa)],[successor]) ).
cnf(c65,plain,
~ member(sK70,suc(sK70)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
member(X0,singleton(X0)),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(d1,plain,
( ~ member(X0,singleton(X1))
| member(X0,suc(X1)) ),
inference(resolution,[status(thm)],[c63,c13]) ).
cnf(d2,plain,
member(X0,suc(X0)),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[d2,c65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/15.40 % Computer : n006.cluster.edu
% 0.08/15.40 % Model : x86_64 x86_64
% 0.08/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/15.40 % Memory : 8046.5625MB
% 0.08/15.40 % OS : Linux 6.8.0-71-generic
% 0.08/15.40 % CPULimit : 300
% 0.08/15.40 % WCLimit : 300
% 0.08/15.40 % DateTime : Sat Sep 26 08:17:42 UTC 2026
% 0.08/15.40 % CPUTime :
% 0.08/15.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.38/19.11 % SZS status Theorem for theBenchmark.p
% 28.38/19.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------