%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET506-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 02:43:21 PM UTC 2026
% Result : Unsatisfiable 51.43s 7.07s
% Output : Proof 51.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 21 unt; 0 def)
% Number of atoms : 91 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 72 ( 33 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 62 ( 9 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f112,negated_conjecture,
universal_class = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_universal_class_not_null_class_1) ).
fof(f112_nnf,plain,
universal_class = null_class,
inference(nnf_transformation,[status(thm)],[f112]) ).
cnf(c112,plain,
universal_class = null_class,
inference(cnf_transformation,[status(esa)],[f112_nnf]) ).
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(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(p113,plain,
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[c0,c3]) ).
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(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(p119,plain,
member(null_class,omega),
inference(resolution,[status(thm)],[c46,c49]) ).
cnf(p154,plain,
member(null_class,universal_class),
inference(resolution,[status(thm)],[p113,p119]) ).
cnf(f8,axiom,
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f8_nnf,plain,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p165,plain,
member(null_class,unordered_pair(null_class,X0)),
inference(resolution,[status(thm)],[p154,c8]) ).
cnf(p170,plain,
member(null_class,unordered_pair(universal_class,X0)),
inference(superposition,[status(thm)],[c112,p165]) ).
cnf(f7,axiom,
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f7_nnf,plain,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p200,plain,
( null_class = X0
| null_class = universal_class ),
inference(resolution,[status(thm)],[p170,c7]) ).
cnf(p203,plain,
null_class = universal_class,
inference(factoring,[status(thm)],[p200]) ).
cnf(f65,axiom,
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f65_nnf,plain,
! [X] :
( member(regular(X),X)
| X = null_class ),
inference(nnf_transformation,[status(thm)],[f65]) ).
fof(f65_sk,plain,
! [X] :
( member(regular(X),X)
| X = null_class ),
inference(skolemisation,[status(esa)],[f65_nnf]) ).
cnf(c65,plain,
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(esa)],[f65_sk]) ).
cnf(p210,plain,
( member(regular(X0),X0)
| X0 = universal_class ),
inference(demodulation,[status(thm)],[p203,c65]) ).
cnf(p355,plain,
( complement(X0) = universal_class
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[c23,p210]) ).
cnf(p215,plain,
( member(regular(X0),universal_class)
| X0 = universal_class ),
inference(resolution,[status(thm)],[p210,p113]) ).
cnf(p3287,plain,
( complement(universal_class) = universal_class
| complement(universal_class) = universal_class ),
inference(resolution,[status(thm)],[p355,p215]) ).
cnf(p3291,plain,
complement(universal_class) = universal_class,
inference(factoring,[status(thm)],[p3287]) ).
cnf(p3305,plain,
( ~ member(X0,universal_class)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[p3291,c23]) ).
cnf(p3311,plain,
~ member(X0,universal_class),
inference(factoring,[status(thm)],[p3305]) ).
cnf(f51,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f51_nnf,plain,
member(omega,universal_class),
inference(nnf_transformation,[status(thm)],[f51]) ).
cnf(c51,plain,
member(omega,universal_class),
inference(cnf_transformation,[status(esa)],[f51_nnf]) ).
cnf(p3312,plain,
$false,
inference(resolution,[status(thm)],[p3311,c51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET506-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n006.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 11:08:11 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 51.43/7.07 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 51.43/7.07 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------