%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET094+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 : n015.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 : Theorem 32.28s 4.68s
% Output : Proof 32.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 14 unt; 0 def)
% Number of atoms : 78 ( 42 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 74 ( 27 ~; 25 |; 18 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 22 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(Y,X)
& subclass(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality) ).
fof(f2_nnf,plain,
! [X,Y] :
( ( ~ subclass(Y,X)
| ~ subclass(X,Y)
| X = Y )
& ( ( subclass(Y,X)
& subclass(X,Y) )
| X != Y ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] :
( ( ~ subclass(Y,X)
| ~ subclass(X,Y)
| X = Y )
& ( ( subclass(Y,X)
& subclass(X,Y) )
| X != Y ) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c6,plain,
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(c5,plain,
( subclass(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f47,conjecture,
! [X,Y] :
( ( member(Y,X)
& singleton(member_of(X)) = X )
=> member_of(X) = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_singletons1_1) ).
fof(f47_neg,negated_conjecture,
~ ! [X,Y] :
( ( member(Y,X)
& singleton(member_of(X)) = X )
=> member_of(X) = Y ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f47_nnf,plain,
? [X,Y] :
( member_of(X) != Y
& member(Y,X)
& singleton(member_of(X)) = X ),
inference(nnf_transformation,[status(thm)],[f47_neg]) ).
fof(f47_sk,plain,
( member_of(sk7) != sk8
& member(sk8,sk7)
& singleton(member_of(sk7)) = sk7 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8])],[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]) ).
cnf(p101,plain,
sk7 = unordered_pair(member_of(sk7),member_of(sk7)),
inference(superposition,[status(thm)],[c93,c12]) ).
cnf(p111,plain,
subclass(unordered_pair(member_of(sk7),member_of(sk7)),sk7),
inference(resolution,[status(thm)],[c5,p101]) ).
cnf(p120,plain,
( ~ subclass(sk7,unordered_pair(member_of(sk7),member_of(sk7)))
| unordered_pair(member_of(sk7),member_of(sk7)) = sk7 ),
inference(resolution,[status(thm)],[c6,p111]) ).
cnf(c4,plain,
( subclass(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p106,plain,
subclass(sk7,unordered_pair(member_of(sk7),member_of(sk7))),
inference(resolution,[status(thm)],[c4,p101]) ).
cnf(p123,plain,
unordered_pair(member_of(sk7),member_of(sk7)) = sk7,
inference(resolution,[status(thm)],[p120,p106]) ).
fof(f3,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f3_nnf,plain,
! [U,X,Y] :
( ( ( U != Y
& U != X )
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ( ( ( U = Y
| U = X )
& member(U,universal_class) )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [U,X,Y] :
( ( ( U != Y
& U != X )
| ~ member(U,universal_class)
| member(U,unordered_pair(X,Y)) )
& ( ( ( U = Y
| U = X )
& member(U,universal_class) )
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c8,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p134,plain,
( X0 = member_of(sk7)
| X0 = member_of(sk7)
| ~ member(X0,sk7) ),
inference(superposition,[status(thm)],[p123,c8]) ).
cnf(p137,plain,
( X0 = member_of(sk7)
| ~ member(X0,sk7) ),
inference(factoring,[status(thm)],[p134]) ).
cnf(c94,plain,
member(sk8,sk7),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(p138,plain,
sk8 = member_of(sk7),
inference(resolution,[status(thm)],[p137,c94]) ).
cnf(c95,plain,
member_of(sk7) != sk8,
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(p148,plain,
sk8 != sk8,
inference(superposition,[status(thm)],[p138,c95]) ).
cnf(p154,plain,
$false,
inference(equality_resolution,[status(thm)],[p148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET094+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n015.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 09:48:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 32.28/4.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.28/4.68 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------