%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET093+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 : n005.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 28.56s 4.12s
% Output : Proof 28.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 13 unt; 0 def)
% Number of atoms : 21 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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 : 16 ( 3 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f47,conjecture,
! [X] :
( singleton(member_of(X)) = X
=> member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_singletons_are_sets) ).
fof(f47_neg,negated_conjecture,
~ ! [X] :
( singleton(member_of(X)) = X
=> member(X,universal_class) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f47_nnf,plain,
? [X] :
( ~ member(X,universal_class)
& singleton(member_of(X)) = X ),
inference(nnf_transformation,[status(thm)],[f47_neg]) ).
fof(f47_sk,plain,
( ~ member(sk7,universal_class)
& singleton(member_of(sk7)) = sk7 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f47_nnf]) ).
cnf(c93,plain,
singleton(member_of(sk7)) = sk7,
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
fof(f5,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f5_nnf,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : singleton(X) = unordered_pair(X,X),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c12,plain,
singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f4,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
fof(f4_nnf,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c11,plain,
member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p99,plain,
member(singleton(X0),universal_class),
inference(superposition,[status(thm)],[c12,c11]) ).
cnf(p102,plain,
member(sk7,universal_class),
inference(superposition,[status(thm)],[c93,p99]) ).
cnf(c94,plain,
~ member(sk7,universal_class),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(p103,plain,
$false,
inference(resolution,[status(thm)],[p102,c94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET093+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n005.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 09:44:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 28.56/4.12 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.56/4.12 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------