%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM409+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 12:28:05 PM UTC 2025
% Result : Theorem 3.60s 0.77s
% Output : CNFRefutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 13
% Syntax : Number of formulae : 50 ( 23 unt; 0 def)
% Number of atoms : 111 ( 4 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 96 ( 35 ~; 30 |; 22 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 25 ( 1 sgn 13 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t45_ordinal1,plain,
! [A] : transfinite_sequence_of(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_ordinal1) ).
fof(t45_ordinal1_negated,plain,
~ ! [A] : transfinite_sequence_of(empty_set,A),
inference(negate_conjecture,[status(cth)],[t45_ordinal1]) ).
cnf(94,plain,
~ transfinite_sequence_of(empty_set,sK22),
inference(cnf,[status(esa)],[t45_ordinal1_negated]) ).
cnf(l0,plain,
~ transfinite_sequence_of(empty_set,sK22),
inference(instantiation,[status(thm)],[94]) ).
fof(d8_ordinal1,plain,
! [A,B] :
( ( relation(B)
& function(B)
& transfinite_sequence(B) )
=> ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
cnf(21,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ transfinite_sequence(X0)
| ~ subset(relation_rng(X0),X1)
| transfinite_sequence_of(X0,X1) ),
inference(cnf,[status(esa)],[d8_ordinal1]) ).
cnf(l1,plain,
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ transfinite_sequence(empty_set)
| ~ subset(relation_rng(empty_set),sK22)
| transfinite_sequence_of(empty_set,sK22) ),
inference(instantiation,[status(thm)],[21]) ).
fof(fc2_ordinal1,plain,
( relation(empty_set)
& relation_empty_yielding(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
cnf(32,plain,
relation(empty_set),
inference(cnf,[status(esa)],[fc2_ordinal1]) ).
cnf(l3,plain,
relation(empty_set),
inference(instantiation,[status(thm)],[32]) ).
fof(d7_ordinal1,plain,
! [A] :
( ( relation(A)
& function(A) )
=> ( transfinite_sequence(A)
<=> ordinal(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_ordinal1) ).
cnf(19,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ ordinal(relation_dom(X0))
| transfinite_sequence(X0) ),
inference(cnf,[status(esa)],[d7_ordinal1]) ).
cnf(l4,plain,
( ~ function(empty_set)
| ~ relation(empty_set)
| ~ ordinal(relation_dom(empty_set))
| transfinite_sequence(empty_set) ),
inference(instantiation,[status(thm)],[19]) ).
fof(cc1_relat_1,plain,
! [A] :
( empty(A)
=> relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
cnf(4,plain,
( ~ empty(X0)
| relation(X0) ),
inference(cnf,[status(esa)],[cc1_relat_1]) ).
cnf(l11,plain,
( ~ empty(empty_set)
| relation(empty_set) ),
inference(instantiation,[status(thm)],[4]) ).
fof(cc3_ordinal1,plain,
! [A] :
( empty(A)
=> ( epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
cnf(9,plain,
( ~ empty(X0)
| ordinal(X0) ),
inference(cnf,[status(esa)],[cc3_ordinal1]) ).
cnf(l6,plain,
( ~ empty(relation_dom(empty_set))
| ordinal(relation_dom(empty_set)) ),
inference(instantiation,[status(thm)],[9]) ).
fof(fc7_relat_1,plain,
! [A] :
( empty(A)
=> ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
cnf(45,plain,
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf,[status(esa)],[fc7_relat_1]) ).
cnf(l48,plain,
( ~ empty(empty_set)
| empty(relation_dom(empty_set)) ),
inference(instantiation,[status(thm)],[45]) ).
cnf(34,plain,
function(empty_set),
inference(cnf,[status(esa)],[fc2_ordinal1]) ).
cnf(l2,plain,
function(empty_set),
inference(instantiation,[status(thm)],[34]) ).
cnf(36,plain,
empty(empty_set),
inference(cnf,[status(esa)],[fc2_ordinal1]) ).
cnf(l53,plain,
empty(empty_set),
inference(instantiation,[status(thm)],[36]) ).
fof(cc1_funct_1,plain,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
cnf(1,plain,
( ~ empty(X0)
| function(X0) ),
inference(cnf,[status(esa)],[cc1_funct_1]) ).
cnf(l28,plain,
( ~ empty(sK13)
| function(sK13) ),
inference(instantiation,[status(thm)],[1]) ).
fof(t2_xboole_1,plain,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
cnf(91,plain,
subset(empty_set,X0),
inference(cnf,[status(esa)],[t2_xboole_1]) ).
cnf(l143,plain,
subset(empty_set,sK22),
inference(instantiation,[status(thm)],[91]) ).
fof(rc2_ordinal1,plain,
? [A] :
( relation(A)
& function(A)
& one_to_one(A)
& empty(A)
& epsilon_transitive(A)
& epsilon_connected(A)
& ordinal(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
cnf(63,plain,
empty(sK13),
inference(cnf,[status(esa)],[rc2_ordinal1]) ).
cnf(l34,plain,
empty(sK13),
inference(instantiation,[status(thm)],[63]) ).
fof(t8_boole,plain,
! [A,B] :
~ ( empty(A)
& A != B
& empty(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
cnf(101,plain,
( ~ empty(X0)
| ~ empty(X1)
| X0 = X1 ),
inference(cnf,[status(esa)],[t8_boole]) ).
cnf(l26,plain,
( ~ empty(sK13)
| ~ empty(empty_set)
| sK13 = empty_set ),
inference(instantiation,[status(thm)],[101]) ).
cnf(l31,plain,
empty(sK13),
inference(instantiation,[status(thm)],[63]) ).
cnf(l27,plain,
empty(empty_set),
inference(instantiation,[status(thm)],[36]) ).
cnf(l16,plain,
empty(empty_set),
inference(instantiation,[status(thm)],[36]) ).
cnf(l128,plain,
( ~ empty(empty_set)
| ~ empty(relation_rng(empty_set))
| empty_set = relation_rng(empty_set) ),
inference(instantiation,[status(thm)],[101]) ).
fof(fc8_relat_1,plain,
! [A] :
( empty(A)
=> ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
cnf(47,plain,
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf,[status(esa)],[fc8_relat_1]) ).
cnf(l131,plain,
( ~ empty(empty_set)
| empty(relation_rng(empty_set)) ),
inference(instantiation,[status(thm)],[47]) ).
cnf(l136,plain,
empty(empty_set),
inference(instantiation,[status(thm)],[36]) ).
fof(fc1_xboole_0,plain,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
cnf(30,plain,
empty(empty_set),
inference(cnf,[status(esa)],[fc1_xboole_0]) ).
cnf(l129,plain,
empty(empty_set),
inference(instantiation,[status(thm)],[30]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l4,l11,l6,l48,l2,l53,l28,l143,l34,l26,l31,l27,l16,l128,l131,l136,l129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM409+1 : TPTP v9.0.0. Released v3.2.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n020.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 21 11:56:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.12/0.36 % launching worker at depth: 11
% 0.18/0.41 % launching worker at depth: 12
% 3.60/0.77 % SZS status Theorem for theBenchmark
% 3.60/0.77 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------