%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : NUM412+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 : n031.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 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 78 ( 32 ~; 29 |; 7 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 3 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t48_ordinal1,plain,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ! [C] :
( ordinal(C)
=> transfinite_sequence_of(tseq_dom_restriction(B,C),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_ordinal1) ).
fof(t48_ordinal1_negated,plain,
~ ! [A,B] :
( transfinite_sequence_of(B,A)
=> ! [C] :
( ordinal(C)
=> transfinite_sequence_of(tseq_dom_restriction(B,C),A) ) ),
inference(negate_conjecture,[status(cth)],[t48_ordinal1]) ).
cnf(87,plain,
transfinite_sequence_of(sK18,sK17),
inference(cnf,[status(esa)],[t48_ordinal1_negated]) ).
cnf(l0,plain,
transfinite_sequence_of(sK18,sK17),
inference(instantiation,[status(thm)],[87]) ).
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(l1,plain,
( ~ function(sK18)
| ~ relation(sK18)
| ~ transfinite_sequence(sK18)
| ~ transfinite_sequence_of(sK18,sK17)
| subset(relation_rng(sK18),sK17) ),
inference(instantiation,[status(thm)],[10]) ).
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(16,plain,
( ~ transfinite_sequence_of(X0,X1)
| transfinite_sequence(X0) ),
inference(cnf,[status(esa)],[dt_m1_ordinal1]) ).
cnf(l9,plain,
( ~ transfinite_sequence_of(sK18,sK17)
| transfinite_sequence(sK18) ),
inference(instantiation,[status(thm)],[16]) ).
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) ).
cnf(86,plain,
( ~ transfinite_sequence_of(X0,X1)
| ~ subset(X1,X2)
| transfinite_sequence_of(X0,X2) ),
inference(cnf,[status(esa)],[t47_ordinal1]) ).
cnf(l4,plain,
( ~ transfinite_sequence_of(tseq_dom_restriction(sK18,sK19),relation_rng(sK18))
| ~ subset(relation_rng(sK18),sK17)
| transfinite_sequence_of(tseq_dom_restriction(sK18,sK19),sK17) ),
inference(instantiation,[status(thm)],[86]) ).
cnf(15,plain,
( ~ transfinite_sequence_of(X0,X1)
| function(X0) ),
inference(cnf,[status(esa)],[dt_m1_ordinal1]) ).
cnf(l2,plain,
( ~ transfinite_sequence_of(sK18,sK17)
| function(sK18) ),
inference(instantiation,[status(thm)],[15]) ).
fof(dt_k2_ordinal1,plain,
! [A,B] :
( ( relation(A)
& function(A)
& transfinite_sequence(A)
& ordinal(B) )
=> transfinite_sequence_of(tseq_dom_restriction(A,B),relation_rng(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_ordinal1) ).
cnf(12,plain,
( ~ function(X0)
| ~ relation(X0)
| ~ ordinal(X1)
| ~ transfinite_sequence(X0)
| transfinite_sequence_of(tseq_dom_restriction(X0,X1),relation_rng(X0)) ),
inference(cnf,[status(esa)],[dt_k2_ordinal1]) ).
cnf(l8,plain,
( ~ function(sK18)
| ~ relation(sK18)
| ~ ordinal(sK19)
| ~ transfinite_sequence(sK18)
| transfinite_sequence_of(tseq_dom_restriction(sK18,sK19),relation_rng(sK18)) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l12,plain,
( ~ transfinite_sequence_of(sK18,sK17)
| function(sK18) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(l45,plain,
( ~ transfinite_sequence_of(sK18,sK17)
| transfinite_sequence(sK18) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(14,plain,
( ~ transfinite_sequence_of(X0,X1)
| relation(X0) ),
inference(cnf,[status(esa)],[dt_m1_ordinal1]) ).
cnf(l26,plain,
( ~ transfinite_sequence_of(sK18,sK17)
| relation(sK18) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(l3,plain,
( ~ transfinite_sequence_of(sK18,sK17)
| relation(sK18) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(89,plain,
~ transfinite_sequence_of(tseq_dom_restriction(sK18,sK19),sK17),
inference(cnf,[status(esa)],[t48_ordinal1_negated]) ).
cnf(l37,plain,
~ transfinite_sequence_of(tseq_dom_restriction(sK18,sK19),sK17),
inference(instantiation,[status(thm)],[89]) ).
cnf(88,plain,
ordinal(sK19),
inference(cnf,[status(esa)],[t48_ordinal1_negated]) ).
cnf(l41,plain,
ordinal(sK19),
inference(instantiation,[status(thm)],[88]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l9,l4,l2,l8,l12,l45,l26,l3,l37,l41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM412+1 : TPTP v9.0.0. Released v3.2.0.
% 0.10/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.33 % Computer : n031.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon Jul 21 11:56:34 EDT 2025
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % launching worker at depth: 1
% 0.14/0.34 % launching worker at depth: 6
% 0.14/0.34 % launching worker at depth: 4
% 0.14/0.34 % launching worker at depth: 3
% 0.14/0.34 % launching worker at depth: 5
% 0.14/0.34 % launching worker at depth: 8
% 0.14/0.34 % launching worker at depth: 7
% 0.14/0.34 % launching worker at depth: 2
% 0.14/0.34 % launching worker at depth: 9
% 0.14/0.34 % launching worker at depth: 10
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------