%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET091+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Fri Sep 25 02:42:11 PM UTC 2026
% Result : Theorem 50.70s 6.99s
% Output : Proof 50.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 8 unt; 0 def)
% Number of atoms : 44 ( 33 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 38 ( 16 ~; 12 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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; 3 con; 0-1 aty)
% Number of variables : 19 ( 0 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
! [X] :
( member_of(X) = X
| singleton(member_of(X)) = X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_self) ).
fof(f46_nnf,plain,
! [X] :
( member_of(X) = X
| singleton(member_of(X)) = X ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [X] :
( member_of(X) = X
| singleton(member_of(X)) = X ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c92,plain,
( member_of(X0) = X0
| singleton(member_of(X0)) = X0 ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
fof(f45,axiom,
! [X] :
( member_of(X) = X
| member(member_of(X),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_universal_self) ).
fof(f45_nnf,plain,
! [X] :
( member_of(X) = X
| member(member_of(X),universal_class) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [X] :
( member_of(X) = X
| member(member_of(X),universal_class) ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c91,plain,
( member_of(X0) = X0
| member(member_of(X0),universal_class) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
fof(f47,conjecture,
! [X,U] :
( ( X = U
& ~ ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) ) )
=> member_of(X) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_when_not_a_singleton) ).
fof(f47_neg,negated_conjecture,
~ ! [X,U] :
( ( X = U
& ~ ? [Y] :
( X = singleton(Y)
& member(Y,universal_class) ) )
=> member_of(X) = U ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f47_nnf,plain,
? [X,U] :
( member_of(X) != U
& X = U
& ! [Y] :
( X != singleton(Y)
| ~ member(Y,universal_class) ) ),
inference(nnf_transformation,[status(thm)],[f47_neg]) ).
fof(f47_sk,plain,
! [Y] :
( member_of(sk7) != sk8
& sk7 = sk8
& ( sk7 != singleton(Y)
| ~ member(Y,universal_class) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8])],[f47_nnf]) ).
cnf(c94,plain,
sk7 = sk8,
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(c95,plain,
member_of(sk7) != sk8,
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(p97,plain,
member_of(sk7) != sk7,
inference(superposition,[status(thm)],[c94,c95]) ).
cnf(p2451,plain,
member(member_of(sk7),universal_class),
inference(resolution,[status(thm)],[c91,p97]) ).
cnf(c93,plain,
( sk7 != singleton(X2)
| ~ member(X2,universal_class) ),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(p2477,plain,
sk7 != singleton(member_of(sk7)),
inference(resolution,[status(thm)],[p2451,c93]) ).
cnf(p2594,plain,
( sk7 != sk7
| member_of(sk7) = sk7 ),
inference(superposition,[status(thm)],[c92,p2477]) ).
cnf(p3088,plain,
member_of(sk7) = sk7,
inference(equality_resolution,[status(thm)],[p2594]) ).
cnf(p3089,plain,
sk7 != sk7,
inference(demodulation,[status(thm)],[p3088,p97]) ).
cnf(p3615,plain,
$false,
inference(equality_resolution,[status(thm)],[p3089]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET091+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n006.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 09:43:27 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 50.70/6.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 50.70/6.99 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------