%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET094-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 4.62s 1.16s
% Output : Proof 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 84 ( 44 unt; 0 def)
% Number of atoms : 132 ( 56 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 134 ( 86 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-4 aty)
% Number of variables : 131 ( 17 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
( subclass(Y,X)
| X != Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass2) ).
fof(f5_nnf,plain,
! [X,Y] :
( subclass(Y,X)
| X != Y ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( subclass(Y,X)
| X != Y ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( subclass(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(X0,X1,subclass(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f137,negated_conjecture,
singleton(member_of(x)) = x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_of_singletons1_1) ).
fof(f137_nnf,plain,
singleton(member_of(x)) = x,
inference(nnf_transformation,[status(thm)],[f137]) ).
cnf(c137,plain,
singleton(member_of(x)) = x,
inference(cnf_transformation,[status(esa)],[f137_nnf]) ).
cnf(hi124,negated_conjecture,
singleton(member_of(x)) = x,
inference(equality_encoding,[status(esa)],[c137]) ).
cnf(f11,axiom,
unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f11_nnf,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X] : unordered_pair(X,X) = singleton(X),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi13,axiom,
unordered_pair(X0,X0) = singleton(X0),
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h191,plain,
subclass(x,unordered_pair(member_of(x),member_of(x))) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi124,hi13]) ).
cnf(f96,axiom,
( subclass(X,Z)
| ~ subclass(Y,Z)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subclass) ).
fof(f96_nnf,plain,
! [X,Y,Z] :
( subclass(X,Z)
| ~ subclass(Y,Z)
| ~ subclass(X,Y) ),
inference(nnf_transformation,[status(thm)],[f96]) ).
fof(f96_sk,plain,
! [X,Y,Z] :
( subclass(X,Z)
| ~ subclass(Y,Z)
| ~ subclass(X,Y) ),
inference(skolemisation,[status(esa)],[f96_nnf]) ).
cnf(c96,plain,
( subclass(X0,X2)
| ~ subclass(X1,X2)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f96_sk]) ).
cnf(hi89,axiom,
ifeq(subclass(X0,X1),true,ifeq(subclass(X1,X2),true,subclass(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c96]) ).
cnf(f109,axiom,
subclass(singleton(Y),unordered_pair(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair2) ).
fof(f109_nnf,plain,
! [Y,X] : subclass(singleton(Y),unordered_pair(X,Y)),
inference(nnf_transformation,[status(thm)],[f109]) ).
fof(f109_sk,plain,
! [Y,X] : subclass(singleton(Y),unordered_pair(X,Y)),
inference(skolemisation,[status(esa)],[f109_nnf]) ).
cnf(c109,plain,
subclass(singleton(X0),unordered_pair(X1,X0)),
inference(cnf_transformation,[status(esa)],[f109_sk]) ).
cnf(hi100,axiom,
subclass(singleton(X0),unordered_pair(X1,X0)) = true,
inference(equality_encoding,[status(esa)],[c109]) ).
cnf(h5203,plain,
subclass(x,unordered_pair(V0,member_of(x))) = true,
inference(hyper_resolution,[status(thm)],[hi89,h191,hi100,hi13]) ).
cnf(f0,axiom,
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f0_nnf,plain,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(subclass(X0,X1),true,ifeq(member(X2,X0),true,member(X2,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f138,negated_conjecture,
member(y,x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_of_singletons1_2) ).
fof(f138_nnf,plain,
member(y,x),
inference(nnf_transformation,[status(thm)],[f138]) ).
cnf(c138,plain,
member(y,x),
inference(cnf_transformation,[status(esa)],[f138_nnf]) ).
cnf(hi125,negated_conjecture,
member(y,x) = true,
inference(equality_encoding,[status(esa)],[c138]) ).
cnf(h5214,plain,
member(y,unordered_pair(V0,member_of(x))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h5203,hi125]) ).
cnf(f124,axiom,
( Y = X
| ~ member(Y,singleton(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f124_nnf,plain,
! [Y,X] :
( Y = X
| ~ member(Y,singleton(X)) ),
inference(nnf_transformation,[status(thm)],[f124]) ).
fof(f124_sk,plain,
! [Y,X] :
( Y = X
| ~ member(Y,singleton(X)) ),
inference(skolemisation,[status(esa)],[f124_nnf]) ).
cnf(c124,plain,
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(cnf_transformation,[status(esa)],[f124_sk]) ).
cnf(hi111,axiom,
ifeq(member(X0,singleton(X1)),true,X0,X1) = X1,
inference(equality_encoding,[status(esa)],[c124]) ).
cnf(h5226,plain,
y = member_of(x),
inference(hyper_resolution,[status(thm)],[hi111,h5214,hi13]) ).
cnf(f139,negated_conjecture,
member_of(x) != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_property_of_singletons1_3) ).
fof(f139_nnf,plain,
member_of(x) != y,
inference(nnf_transformation,[status(thm)],[f139]) ).
fof(f139_sk,plain,
member_of(x) != y,
inference(skolemisation,[status(esa)],[f139_nnf]) ).
cnf(c139,plain,
member_of(x) != y,
inference(cnf_transformation,[status(esa)],[f139_sk]) ).
cnf(hi134,negated_conjecture,
ifeq(member_of(x),y,false,true) = true,
inference(equality_encoding,[status(esa)],[c139]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi134,h5226]) ).
cnf(t680,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f23,axiom,
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f23_nnf,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(f29,axiom,
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f29_nnf,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(f101,axiom,
~ member(Y,intersection(complement(X),X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',special_classes_lemma) ).
fof(f101_nnf,plain,
! [Y,X] : ~ member(Y,intersection(complement(X),X)),
inference(nnf_transformation,[status(thm)],[f101]) ).
fof(f101_sk,plain,
! [Y,X] : ~ member(Y,intersection(complement(X),X)),
inference(skolemisation,[status(esa)],[f101_nnf]) ).
cnf(c101,plain,
~ member(X0,intersection(complement(X1),X1)),
inference(cnf_transformation,[status(esa)],[f101_sk]) ).
cnf(f102,axiom,
~ member(Z,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f102_nnf,plain,
! [Z] : ~ member(Z,null_class),
inference(nnf_transformation,[status(thm)],[f102]) ).
fof(f102_sk,plain,
! [Z] : ~ member(Z,null_class),
inference(skolemisation,[status(esa)],[f102_nnf]) ).
cnf(c102,plain,
~ member(X0,null_class),
inference(cnf_transformation,[status(esa)],[f102_sk]) ).
cnf(f115,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).
fof(f115_nnf,plain,
! [X,Y] :
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f115]) ).
fof(f115_sk,plain,
! [X,Y] :
( unordered_pair(X,Y) != null_class
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f115_nnf]) ).
cnf(c115,plain,
( unordered_pair(X0,X1) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f115_sk]) ).
cnf(f116,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
fof(f116_nnf,plain,
! [Y,X] :
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
inference(nnf_transformation,[status(thm)],[f116]) ).
fof(f116_sk,plain,
! [Y,X] :
( unordered_pair(X,Y) != null_class
| ~ member(Y,universal_class) ),
inference(skolemisation,[status(esa)],[f116_nnf]) ).
cnf(c116,plain,
( unordered_pair(X1,X0) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f116_sk]) ).
cnf(f117,axiom,
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom3) ).
fof(f117_nnf,plain,
! [X,Y,U,V] :
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
inference(nnf_transformation,[status(thm)],[f117]) ).
fof(f117_sk,plain,
! [X,Y,U,V] :
( unordered_pair(X,Y) != null_class
| ~ member(ordered_pair(X,Y),cross_product(U,V)) ),
inference(skolemisation,[status(esa)],[f117_nnf]) ).
cnf(c117,plain,
( unordered_pair(X0,X1) != null_class
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f117_sk]) ).
cnf(f122,axiom,
( singleton(X) != null_class
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_set_in_its_singleton) ).
fof(f122_nnf,plain,
! [X] :
( singleton(X) != null_class
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f122]) ).
fof(f122_sk,plain,
! [X] :
( singleton(X) != null_class
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f122_nnf]) ).
cnf(c122,plain,
( singleton(X0) != null_class
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f122_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c101,c102,c115,c116,c117,c122,c139]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t680]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET094-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 09:49:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.62/1.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.62/1.16 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------