%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM411+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 : n027.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 0.19s 0.42s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 13 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 74 ( 32 ~; 29 |; 5 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 26 ( 3 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t47_ordinal1,plain,
! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_ordinal1) ).
fof(t47_ordinal1_negated,plain,
~ ! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
inference(negate_conjecture,[status(cth)],[t47_ordinal1]) ).
cnf(80,plain,
subset(sK17,sK18),
inference(cnf,[status(esa)],[t47_ordinal1_negated]) ).
cnf(l0,plain,
subset(sK17,sK18),
inference(instantiation,[status(thm)],[80]) ).
fof(t1_xboole_1,plain,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
cnf(76,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| subset(X0,X2) ),
inference(cnf,[status(esa)],[t1_xboole_1]) ).
cnf(l1,plain,
( ~ subset(relation_rng(sK19),sK17)
| ~ subset(sK17,sK18)
| subset(relation_rng(sK19),sK18) ),
inference(instantiation,[status(thm)],[76]) ).
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(10,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ transfinite_sequence(X0)
| ~ transfinite_sequence_of(X0,X1)
| subset(relation_rng(X0),X1) ),
inference(cnf,[status(esa)],[d8_ordinal1]) ).
cnf(l39,plain,
( ~ function(sK19)
| ~ relation(sK19)
| ~ transfinite_sequence(sK19)
| ~ transfinite_sequence_of(sK19,sK17)
| subset(relation_rng(sK19),sK17) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(11,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(l3,plain,
( ~ function(sK19)
| ~ relation(sK19)
| ~ transfinite_sequence(sK19)
| ~ subset(relation_rng(sK19),sK18)
| transfinite_sequence_of(sK19,sK18) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(82,plain,
~ transfinite_sequence_of(sK19,sK18),
inference(cnf,[status(esa)],[t47_ordinal1_negated]) ).
cnf(l72,plain,
~ transfinite_sequence_of(sK19,sK18),
inference(instantiation,[status(thm)],[82]) ).
fof(dt_m1_ordinal1,plain,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ( relation(B)
& function(B)
& transfinite_sequence(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
cnf(14,plain,
( ~ transfinite_sequence_of(X0,X1)
| transfinite_sequence(X0) ),
inference(cnf,[status(esa)],[dt_m1_ordinal1]) ).
cnf(l20,plain,
( ~ transfinite_sequence_of(sK19,sK17)
| transfinite_sequence(sK19) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(13,plain,
( ~ transfinite_sequence_of(X0,X1)
| function(X0) ),
inference(cnf,[status(esa)],[dt_m1_ordinal1]) ).
cnf(l40,plain,
( ~ transfinite_sequence_of(sK19,sK17)
| function(sK19) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l66,plain,
( ~ transfinite_sequence_of(sK19,sK17)
| transfinite_sequence(sK19) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(81,plain,
transfinite_sequence_of(sK19,sK17),
inference(cnf,[status(esa)],[t47_ordinal1_negated]) ).
cnf(l67,plain,
transfinite_sequence_of(sK19,sK17),
inference(instantiation,[status(thm)],[81]) ).
cnf(l68,plain,
transfinite_sequence_of(sK19,sK17),
inference(instantiation,[status(thm)],[81]) ).
cnf(12,plain,
( ~ transfinite_sequence_of(X0,X1)
| relation(X0) ),
inference(cnf,[status(esa)],[dt_m1_ordinal1]) ).
cnf(l5,plain,
( ~ transfinite_sequence_of(sK19,sK17)
| relation(sK19) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l7,plain,
transfinite_sequence_of(sK19,sK17),
inference(instantiation,[status(thm)],[81]) ).
cnf(l14,plain,
( ~ transfinite_sequence_of(sK19,sK17)
| function(sK19) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l45,plain,
transfinite_sequence_of(sK19,sK17),
inference(instantiation,[status(thm)],[81]) ).
cnf(l16,plain,
transfinite_sequence_of(sK19,sK17),
inference(instantiation,[status(thm)],[81]) ).
cnf(l27,plain,
transfinite_sequence_of(sK19,sK17),
inference(instantiation,[status(thm)],[81]) ).
cnf(l56,plain,
( ~ transfinite_sequence_of(sK19,sK17)
| relation(sK19) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l57,plain,
transfinite_sequence_of(sK19,sK17),
inference(instantiation,[status(thm)],[81]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l39,l3,l72,l20,l40,l66,l67,l68,l5,l7,l14,l45,l16,l27,l56,l57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM411+1 : TPTP v9.0.0. Released v3.2.0.
% 0.06/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Jul 21 11:56:49 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % launching worker at depth: 5
% 0.12/0.35 % launching worker at depth: 4
% 0.12/0.35 % launching worker at depth: 1
% 0.12/0.35 % launching worker at depth: 3
% 0.12/0.35 % launching worker at depth: 6
% 0.12/0.35 % launching worker at depth: 2
% 0.12/0.35 % launching worker at depth: 7
% 0.12/0.35 % launching worker at depth: 8
% 0.12/0.35 % launching worker at depth: 9
% 0.12/0.35 % launching worker at depth: 10
% 0.12/0.37 % launching worker at depth: 11
% 0.19/0.42 % SZS status Theorem for theBenchmark
% 0.19/0.42 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------