%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET065-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 02:41:55 PM UTC 2026
% Result : Unsatisfiable 3.46s 0.89s
% Output : Proof 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 35 unt; 0 def)
% Number of atoms : 71 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 42 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 59 ( 9 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f106,negated_conjecture,
~ member(null_class,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_class_is_a_set_1) ).
fof(f106_nnf,plain,
~ member(null_class,universal_class),
inference(nnf_transformation,[status(thm)],[f106]) ).
fof(f106_sk,plain,
~ member(null_class,universal_class),
inference(skolemisation,[status(esa)],[f106_nnf]) ).
cnf(c106,plain,
~ member(null_class,universal_class),
inference(cnf_transformation,[status(esa)],[f106_sk]) ).
cnf(t73,plain,
ifeq(member(null_class,universal_class),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c106]) ).
cnf(f46,axiom,
( member(null_class,X)
| ~ inductive(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
fof(f46_nnf,plain,
! [X] :
( member(null_class,X)
| ~ inductive(X) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [X] :
( member(null_class,X)
| ~ inductive(X) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c46,plain,
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(hi38,axiom,
ifeq(inductive(X0),true,member(null_class,X0),true) = true,
inference(equality_encoding,[status(esa)],[c46]) ).
cnf(f49,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f49_nnf,plain,
inductive(omega),
inference(nnf_transformation,[status(thm)],[f49]) ).
cnf(c49,plain,
inductive(omega),
inference(cnf_transformation,[status(esa)],[f49_nnf]) ).
cnf(hi44,axiom,
inductive(omega) = true,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(h1,plain,
member(null_class,omega) = true,
inference(hyper_resolution,[status(thm)],[hi38,hi44]) ).
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(f3,axiom,
subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f3_nnf,plain,
! [X] : subclass(X,universal_class),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : subclass(X,universal_class),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
subclass(X0,universal_class),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
subclass(X0,universal_class) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t9,plain,
member(null_class,universal_class) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi3,h1]) ).
cnf(t183,plain,
member(null_class,universal_class) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(t483,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t73,t183]) ).
cnf(t29,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t173,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t29]) ).
cnf(t484,plain,
false = true,
inference(step,[status(thm)],[t483,t173]) ).
cnf(t477,plain,
false = true,
inference(orient,[status(thm)],[t484]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c23,c29,c101,c102,c106]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t477]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET065-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Thu Sep 24 09:32:36 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.46/0.89 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.46/0.89 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------