%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM409+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 02:19:57 PM UTC 2026
% Result : Theorem 16.91s 2.78s
% Output : Proof 16.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 20 unt; 0 def)
% Number of atoms : 148 ( 6 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 147 ( 52 ~; 48 |; 40 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 36 ( 2 sgn 23 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f48,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f48_nnf,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c101,plain,
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
fof(f24,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f24_nnf,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c49,plain,
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f15,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(f15_nnf,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c29,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p410,plain,
empty(relation_rng(empty_set)),
inference(resolution,[status(thm)],[c49,c29]) ).
cnf(p655,plain,
relation_rng(empty_set) = empty_set,
inference(resolution,[status(thm)],[c101,p410]) ).
fof(f11,axiom,
! [A,B] :
( ( transfinite_sequence(B)
& function(B)
& relation(B) )
=> ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(f11_nnf,plain,
! [A,B] :
( ( ( ~ subset(relation_rng(B),A)
| transfinite_sequence_of(B,A) )
& ( subset(relation_rng(B),A)
| ~ transfinite_sequence_of(B,A) ) )
| ~ transfinite_sequence(B)
| ~ function(B)
| ~ relation(B) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [B,A] :
( ( ( ~ subset(relation_rng(B),A)
| transfinite_sequence_of(B,A) )
& ( subset(relation_rng(B),A)
| ~ transfinite_sequence_of(B,A) ) )
| ~ transfinite_sequence(B)
| ~ function(B)
| ~ relation(B) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c23,plain,
( ~ subset(relation_rng(X1),X0)
| transfinite_sequence_of(X1,X0)
| ~ transfinite_sequence(X1)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(c30,plain,
relation(empty_set),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p294,plain,
( ~ subset(relation_rng(empty_set),X0)
| transfinite_sequence_of(empty_set,X0)
| ~ transfinite_sequence(empty_set)
| ~ function(empty_set) ),
inference(resolution,[status(thm)],[c23,c30]) ).
cnf(p656,plain,
( ~ subset(empty_set,X0)
| transfinite_sequence_of(empty_set,X0)
| ~ transfinite_sequence(empty_set)
| ~ function(empty_set) ),
inference(demodulation,[status(thm)],[p655,p294]) ).
fof(f18,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(f18_nnf,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c36,plain,
function(empty_set),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p807,plain,
( ~ subset(empty_set,X0)
| transfinite_sequence_of(empty_set,X0)
| ~ transfinite_sequence(empty_set) ),
inference(resolution,[status(thm)],[p656,c36]) ).
fof(f23,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f23_nnf,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c47,plain,
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p196,plain,
empty(relation_dom(empty_set)),
inference(resolution,[status(thm)],[c47,c29]) ).
cnf(p617,plain,
relation_dom(empty_set) = empty_set,
inference(resolution,[status(thm)],[c101,p196]) ).
fof(f10,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( transfinite_sequence(A)
<=> ordinal(relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_ordinal1) ).
fof(f10_nnf,plain,
! [A] :
( ( ( ~ ordinal(relation_dom(A))
| transfinite_sequence(A) )
& ( ordinal(relation_dom(A))
| ~ transfinite_sequence(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] :
( ( ( ~ ordinal(relation_dom(A))
| transfinite_sequence(A) )
& ( ordinal(relation_dom(A))
| ~ transfinite_sequence(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c21,plain,
( ~ ordinal(relation_dom(X0))
| transfinite_sequence(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p250,plain,
( ~ ordinal(relation_dom(empty_set))
| transfinite_sequence(empty_set)
| ~ function(empty_set) ),
inference(resolution,[status(thm)],[c21,c30]) ).
cnf(p629,plain,
( ~ ordinal(empty_set)
| transfinite_sequence(empty_set)
| ~ function(empty_set) ),
inference(demodulation,[status(thm)],[p617,p250]) ).
cnf(p701,plain,
( ~ ordinal(empty_set)
| transfinite_sequence(empty_set) ),
inference(resolution,[status(thm)],[p629,c36]) ).
cnf(c41,plain,
ordinal(empty_set),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p702,plain,
transfinite_sequence(empty_set),
inference(resolution,[status(thm)],[p701,c41]) ).
cnf(p808,plain,
( ~ subset(empty_set,X0)
| transfinite_sequence_of(empty_set,X0) ),
inference(resolution,[status(thm)],[p807,p702]) ).
fof(f42,axiom,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f42_nnf,plain,
! [A] : subset(empty_set,A),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [A] : subset(empty_set,A),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c93,plain,
subset(empty_set,X0),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(p810,plain,
transfinite_sequence_of(empty_set,X0),
inference(resolution,[status(thm)],[p808,c93]) ).
fof(f44,conjecture,
! [A] : transfinite_sequence_of(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_ordinal1) ).
fof(f44_neg,negated_conjecture,
~ ! [A] : transfinite_sequence_of(empty_set,A),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f44_nnf,plain,
? [A] : ~ transfinite_sequence_of(empty_set,A),
inference(nnf_transformation,[status(thm)],[f44_neg]) ).
fof(f44_sk,plain,
~ transfinite_sequence_of(empty_set,sk19),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk19])],[f44_nnf]) ).
cnf(c96,plain,
~ transfinite_sequence_of(empty_set,sk19),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(p811,plain,
$false,
inference(resolution,[status(thm)],[p810,c96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM409+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 03:56:53 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.91/2.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.91/2.78 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------