%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET084+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 02:42:06 PM UTC 2026
% Result : Theorem 49.72s 7.64s
% Output : Proof 49.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 17 unt; 0 def)
% Number of atoms : 108 ( 43 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 105 ( 39 ~; 38 |; 23 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 5 sgn 34 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [U,V,X,Y] :
( member(ordered_pair(U,V),cross_product(X,Y))
<=> ( member(V,Y)
& member(U,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_defn) ).
fof(f7_nnf,plain,
! [U,V,X,Y] :
( ( ~ member(V,Y)
| ~ member(U,X)
| member(ordered_pair(U,V),cross_product(X,Y)) )
& ( ( member(V,Y)
& member(U,X) )
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U,V,X,Y] :
( ( ~ member(V,Y)
| ~ member(U,X)
| member(ordered_pair(U,V),cross_product(X,Y)) )
& ( ( member(V,Y)
& member(U,X) )
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c16,plain,
( ~ member(X1,X3)
| ~ member(X0,X2)
| member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f43,conjecture,
! [X,Y] :
( ( member(Y,universal_class)
& singleton(X) = singleton(Y) )
=> X = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_identified_by_element2) ).
fof(f43_neg,negated_conjecture,
~ ! [X,Y] :
( ( member(Y,universal_class)
& singleton(X) = singleton(Y) )
=> X = Y ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f43_nnf,plain,
? [X,Y] :
( X != Y
& member(Y,universal_class)
& singleton(X) = singleton(Y) ),
inference(nnf_transformation,[status(thm)],[f43_neg]) ).
fof(f43_sk,plain,
( sk7 != sk8
& member(sk8,universal_class)
& singleton(sk7) = singleton(sk8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7,sk8])],[f43_nnf]) ).
cnf(c90,plain,
member(sk8,universal_class),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p182,plain,
( ~ member(X0,X1)
| member(ordered_pair(sk8,X0),cross_product(universal_class,X1)) ),
inference(resolution,[status(thm)],[c16,c90]) ).
fof(f5,axiom,
! [X] : singleton(X) = unordered_pair(X,X),
file('/export/starexec/sandbox2/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(f3,axiom,
! [U,X,Y] :
( member(U,unordered_pair(X,Y))
<=> ( ( U = Y
| U = X )
& member(U,universal_class) ) ),
file('/export/starexec/sandbox2/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(c9,plain,
( X0 != X1
| ~ member(X0,universal_class)
| member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p135,plain,
( sk8 != X0
| member(sk8,unordered_pair(X0,X1)) ),
inference(resolution,[status(thm)],[c9,c90]) ).
cnf(p140,plain,
member(sk8,unordered_pair(sk8,X0)),
inference(equality_resolution,[status(thm)],[p135]) ).
cnf(p141,plain,
member(sk8,singleton(sk7)),
inference(superposition,[status(thm)],[c12,p140]) ).
cnf(p196,plain,
member(ordered_pair(sk8,sk7),cross_product(universal_class,singleton(sk7))),
inference(resolution,[status(thm)],[p182,p141]) ).
cnf(c15,plain,
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p215,plain,
member(sk7,singleton(sk7)),
inference(resolution,[status(thm)],[p196,c15]) ).
fof(f2,axiom,
! [X,Y] :
( X = Y
<=> ( subclass(Y,X)
& subclass(X,Y) ) ),
file('/export/starexec/sandbox2/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]) ).
cnf(c89,plain,
singleton(sk7) = singleton(sk8),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p97,plain,
singleton(sk7) = unordered_pair(sk8,sk8),
inference(superposition,[status(thm)],[c89,c12]) ).
cnf(p107,plain,
subclass(unordered_pair(sk8,sk8),singleton(sk7)),
inference(resolution,[status(thm)],[c5,p97]) ).
cnf(p116,plain,
( ~ subclass(singleton(sk7),unordered_pair(sk8,sk8))
| unordered_pair(sk8,sk8) = singleton(sk7) ),
inference(resolution,[status(thm)],[c6,p107]) ).
cnf(c4,plain,
( subclass(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p103,plain,
subclass(singleton(sk7),unordered_pair(sk8,sk8)),
inference(resolution,[status(thm)],[c4,p97]) ).
cnf(p118,plain,
unordered_pair(sk8,sk8) = singleton(sk7),
inference(resolution,[status(thm)],[p116,p103]) ).
cnf(c8,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p126,plain,
( X0 = sk8
| X0 = sk8
| ~ member(X0,singleton(sk7)) ),
inference(superposition,[status(thm)],[p118,c8]) ).
cnf(p127,plain,
( X0 = sk8
| ~ member(X0,singleton(sk7)) ),
inference(factoring,[status(thm)],[p126]) ).
cnf(p218,plain,
sk7 = sk8,
inference(resolution,[status(thm)],[p215,p127]) ).
cnf(c91,plain,
sk7 != sk8,
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(p222,plain,
$false,
inference(resolution,[status(thm)],[p218,c91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET084+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 09:38:38 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 49.72/7.64 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 49.72/7.64 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------