%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:43:59 PM UTC 2026
% Result : Theorem 27.85s 4.41s
% Output : Proof 27.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 54 ( 6 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 54 ( 21 ~; 18 |; 10 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 35 ( 2 sgn 23 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,axiom,
! [A,X] :
( member(X,suc(A))
<=> member(X,union(A,singleton(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
fof(f18_nnf,plain,
! [A,X] :
( ( ~ member(X,union(A,singleton(A)))
| member(X,suc(A)) )
& ( member(X,union(A,singleton(A)))
| ~ member(X,suc(A)) ) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,A] :
( ( ~ member(X,union(A,singleton(A)))
| member(X,suc(A)) )
& ( member(X,union(A,singleton(A)))
| ~ member(X,suc(A)) ) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c77,plain,
( ~ member(X1,union(X0,singleton(X0)))
| member(X1,suc(X0)) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f4,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f4_nnf,plain,
! [X,A,B] :
( ( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,A,B] :
( ( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c13,plain,
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f7,axiom,
! [X,A] :
( member(X,singleton(A))
<=> X = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
fof(f7_nnf,plain,
! [X,A] :
( ( X != A
| member(X,singleton(A)) )
& ( X = A
| ~ member(X,singleton(A)) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,A] :
( ( X != A
| member(X,singleton(A)) )
& ( X = A
| ~ member(X,singleton(A)) ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c19,plain,
( X0 != X1
| member(X0,singleton(X1)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p97,plain,
member(X0,singleton(X0)),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(p130,plain,
member(X0,union(X1,singleton(X0))),
inference(resolution,[status(thm)],[c13,p97]) ).
cnf(p2143,plain,
member(X0,suc(X0)),
inference(resolution,[status(thm)],[c77,p130]) ).
fof(f19,conjecture,
! [A] :
( member(A,on)
=> member(A,suc(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thV12) ).
fof(f19_neg,negated_conjecture,
~ ! [A] :
( member(A,on)
=> member(A,suc(A)) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f19_nnf,plain,
? [A] :
( ~ member(A,suc(A))
& member(A,on) ),
inference(nnf_transformation,[status(thm)],[f19_neg]) ).
fof(f19_sk,plain,
( ~ member(sk13,suc(sk13))
& member(sk13,on) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk13])],[f19_nnf]) ).
cnf(c79,plain,
~ member(sk13,suc(sk13)),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p2193,plain,
$false,
inference(resolution,[status(thm)],[p2143,c79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET813+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Thu Sep 24 12:02:04 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.85/4.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.85/4.41 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------