%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET094-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 02:42:12 PM UTC 2026
% Result : Unsatisfiable 49.56s 7.86s
% Output : Proof 49.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 13 unt; 0 def)
% Number of atoms : 29 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 11 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 15 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f91,negated_conjecture,
singleton(member_of(x)) = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_singletons1_1) ).
fof(f91_nnf,plain,
singleton(member_of(x)) = x,
inference(nnf_transformation,[status(thm)],[f91]) ).
cnf(c91,plain,
singleton(member_of(x)) = x,
inference(cnf_transformation,[status(esa)],[f91_nnf]) ).
cnf(f7,axiom,
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f7_nnf,plain,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p108,plain,
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(factoring,[status(thm)],[c7]) ).
cnf(p2403,plain,
( X0 = member_of(x)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c91,p108]) ).
cnf(f92,negated_conjecture,
member(y,x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_singletons1_2) ).
fof(f92_nnf,plain,
member(y,x),
inference(nnf_transformation,[status(thm)],[f92]) ).
cnf(c92,plain,
member(y,x),
inference(cnf_transformation,[status(esa)],[f92_nnf]) ).
cnf(p2472,plain,
y = member_of(x),
inference(resolution,[status(thm)],[p2403,c92]) ).
cnf(f93,negated_conjecture,
member_of(x) != y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_singletons1_3) ).
fof(f93_nnf,plain,
member_of(x) != y,
inference(nnf_transformation,[status(thm)],[f93]) ).
fof(f93_sk,plain,
member_of(x) != y,
inference(skolemisation,[status(esa)],[f93_nnf]) ).
cnf(c93,plain,
member_of(x) != y,
inference(cnf_transformation,[status(esa)],[f93_sk]) ).
cnf(p2482,plain,
y != y,
inference(superposition,[status(thm)],[p2472,c93]) ).
cnf(p2552,plain,
$false,
inference(equality_resolution,[status(thm)],[p2482]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET094-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n026.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 : Thu Sep 24 09:47:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 49.56/7.86 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 49.56/7.86 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------