%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM410+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n021.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 0.09s 0.30s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 13 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 44 ( 17 ~; 14 |; 5 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 11 ( 1 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t46_ordinal1,plain,
! [A] :
( ( relation(A)
& function(A) )
=> ( ordinal(relation_dom(A))
=> transfinite_sequence_of(A,relation_rng(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_ordinal1) ).
fof(t46_ordinal1_negated,plain,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ( ordinal(relation_dom(A))
=> transfinite_sequence_of(A,relation_rng(A)) ) ),
inference(negate_conjecture,[status(cth)],[t46_ordinal1]) ).
cnf(84,plain,
relation(sK17),
inference(cnf,[status(esa)],[t46_ordinal1_negated]) ).
cnf(l0,plain,
relation(sK17),
inference(instantiation,[status(thm)],[84]) ).
fof(d7_ordinal1,plain,
! [A] :
( ( relation(A)
& function(A) )
=> ( transfinite_sequence(A)
<=> ordinal(relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_ordinal1) ).
cnf(11,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ ordinal(relation_dom(X0))
| transfinite_sequence(X0) ),
inference(cnf,[status(esa)],[d7_ordinal1]) ).
cnf(l1,plain,
( ~ function(sK17)
| ~ relation(sK17)
| ~ ordinal(relation_dom(sK17))
| transfinite_sequence(sK17) ),
inference(instantiation,[status(thm)],[11]) ).
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/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).
cnf(13,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(l4,plain,
( ~ function(sK17)
| ~ relation(sK17)
| ~ transfinite_sequence(sK17)
| ~ subset(relation_rng(sK17),relation_rng(sK17))
| transfinite_sequence_of(sK17,relation_rng(sK17)) ),
inference(instantiation,[status(thm)],[13]) ).
fof(reflexivity_r1_tarski,plain,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
cnf(79,plain,
subset(X0,X0),
inference(cnf,[status(esa)],[reflexivity_r1_tarski]) ).
cnf(l6,plain,
subset(relation_rng(sK17),relation_rng(sK17)),
inference(instantiation,[status(thm)],[79]) ).
cnf(85,plain,
function(sK17),
inference(cnf,[status(esa)],[t46_ordinal1_negated]) ).
cnf(l9,plain,
function(sK17),
inference(instantiation,[status(thm)],[85]) ).
cnf(87,plain,
~ transfinite_sequence_of(sK17,relation_rng(sK17)),
inference(cnf,[status(esa)],[t46_ordinal1_negated]) ).
cnf(l11,plain,
~ transfinite_sequence_of(sK17,relation_rng(sK17)),
inference(instantiation,[status(thm)],[87]) ).
cnf(l2,plain,
function(sK17),
inference(instantiation,[status(thm)],[85]) ).
cnf(86,plain,
ordinal(relation_dom(sK17)),
inference(cnf,[status(esa)],[t46_ordinal1_negated]) ).
cnf(l3,plain,
ordinal(relation_dom(sK17)),
inference(instantiation,[status(thm)],[86]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l4,l6,l9,l11,l2,l3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : NUM410+1 : TPTP v9.0.0. Released v3.2.0.
% 0.04/0.09 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.29 % Computer : n021.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Jul 21 11:56:34 EDT 2025
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % launching worker at depth: 1
% 0.09/0.30 % launching worker at depth: 3
% 0.09/0.30 % launching worker at depth: 2
% 0.09/0.30 % launching worker at depth: 4
% 0.09/0.30 % launching worker at depth: 5
% 0.09/0.30 % launching worker at depth: 6
% 0.09/0.30 % launching worker at depth: 7
% 0.09/0.30 % launching worker at depth: 8
% 0.09/0.30 % launching worker at depth: 9
% 0.09/0.30 % launching worker at depth: 10
% 0.09/0.30 % SZS status Theorem for theBenchmark
% 0.09/0.30 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------