%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU323+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 03:45:11 PM UTC 2025
% Result : Theorem 3.61s 0.76s
% Output : CNFRefutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 14 unt; 0 def)
% Number of atoms : 75 ( 3 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 71 ( 28 ~; 25 |; 8 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t51_tops_1,plain,
! [A] :
( ( topological_space(A)
& top_str(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> open_subset(interior(A,B),A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t51_tops_1) ).
fof(t51_tops_1_negated,plain,
~ ! [A] :
( ( topological_space(A)
& top_str(A) )
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> open_subset(interior(A,B),A) ) ),
inference(negate_conjecture,[status(cth)],[t51_tops_1]) ).
cnf(19,plain,
topological_space(sK6),
inference(cnf,[status(esa)],[t51_tops_1_negated]) ).
cnf(l0,plain,
topological_space(sK6),
inference(instantiation,[status(thm)],[19]) ).
fof(fc3_tops_1,plain,
! [A,B] :
( ( topological_space(A)
& top_str(A)
& closed_subset(B,A)
& element(B,powerset(the_carrier(A))) )
=> open_subset(subset_complement(the_carrier(A),B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_tops_1) ).
cnf(0,plain,
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf,[status(esa)],[fc3_tops_1]) ).
cnf(l1,plain,
( ~ top_str(sK6)
| ~ topological_space(sK6)
| ~ closed_subset(topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7)),sK6)
| ~ element(topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7)),powerset(the_carrier(sK6)))
| open_subset(subset_complement(the_carrier(sK6),topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7))),sK6) ),
inference(instantiation,[status(thm)],[0]) ).
fof(fc2_tops_1,plain,
! [A,B] :
( ( topological_space(A)
& top_str(A)
& element(B,powerset(the_carrier(A))) )
=> closed_subset(topstr_closure(A,B),A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_tops_1) ).
cnf(8,plain,
( ~ top_str(X0)
| ~ topological_space(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| closed_subset(topstr_closure(X0,X1),X0) ),
inference(cnf,[status(esa)],[fc2_tops_1]) ).
cnf(l3,plain,
( ~ top_str(sK6)
| ~ topological_space(sK6)
| ~ element(subset_complement(the_carrier(sK6),sK7),powerset(the_carrier(sK6)))
| closed_subset(topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7)),sK6) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(20,plain,
top_str(sK6),
inference(cnf,[status(esa)],[t51_tops_1_negated]) ).
cnf(l34,plain,
top_str(sK6),
inference(instantiation,[status(thm)],[20]) ).
cnf(l2,plain,
top_str(sK6),
inference(instantiation,[status(thm)],[20]) ).
fof(dt_k6_pre_topc,plain,
! [A,B] :
( ( top_str(A)
& element(B,powerset(the_carrier(A))) )
=> element(topstr_closure(A,B),powerset(the_carrier(A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
cnf(7,plain,
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| element(topstr_closure(X0,X1),powerset(the_carrier(X0))) ),
inference(cnf,[status(esa)],[dt_k6_pre_topc]) ).
cnf(l125,plain,
( ~ top_str(sK6)
| ~ element(subset_complement(the_carrier(sK6),sK7),powerset(the_carrier(sK6)))
| element(topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7)),powerset(the_carrier(sK6))) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l135,plain,
top_str(sK6),
inference(instantiation,[status(thm)],[20]) ).
cnf(22,plain,
~ open_subset(interior(sK6,sK7),sK6),
inference(cnf,[status(esa)],[t51_tops_1_negated]) ).
cnf(l186,plain,
~ open_subset(interior(sK6,sK7),sK6),
inference(instantiation,[status(thm)],[22]) ).
fof(d1_tops_1,plain,
! [A] :
( top_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> interior(A,B) = subset_complement(the_carrier(A),topstr_closure(A,subset_complement(the_carrier(A),B))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
cnf(18,plain,
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ),
inference(cnf,[status(esa)],[d1_tops_1]) ).
cnf(l226,plain,
( ~ top_str(sK6)
| ~ element(sK7,powerset(the_carrier(sK6)))
| interior(sK6,sK7) = subset_complement(the_carrier(sK6),topstr_closure(sK6,subset_complement(the_carrier(sK6),sK7))) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(21,plain,
element(sK7,powerset(the_carrier(sK6))),
inference(cnf,[status(esa)],[t51_tops_1_negated]) ).
cnf(l235,plain,
element(sK7,powerset(the_carrier(sK6))),
inference(instantiation,[status(thm)],[21]) ).
cnf(l229,plain,
top_str(sK6),
inference(instantiation,[status(thm)],[20]) ).
fof(dt_k3_subset_1,plain,
! [A,B] :
( element(B,powerset(A))
=> element(subset_complement(A,B),powerset(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
cnf(6,plain,
( ~ element(X0,powerset(X1))
| element(subset_complement(X1,X0),powerset(X1)) ),
inference(cnf,[status(esa)],[dt_k3_subset_1]) ).
cnf(l126,plain,
( ~ element(sK7,powerset(the_carrier(sK6)))
| element(subset_complement(the_carrier(sK6),sK7),powerset(the_carrier(sK6))) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l46,plain,
( ~ element(sK7,powerset(the_carrier(sK6)))
| element(subset_complement(the_carrier(sK6),sK7),powerset(the_carrier(sK6))) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l58,plain,
element(sK7,powerset(the_carrier(sK6))),
inference(instantiation,[status(thm)],[21]) ).
cnf(l127,plain,
element(sK7,powerset(the_carrier(sK6))),
inference(instantiation,[status(thm)],[21]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l34,l2,l125,l135,l186,l226,l235,l229,l126,l46,l58,l127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.09 % Problem : SEU323+1 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.09 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.29 % Computer : n019.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 : Tue Jul 22 00:49:04 EDT 2025
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % launching worker at depth: 2
% 0.09/0.29 % launching worker at depth: 1
% 0.09/0.29 % launching worker at depth: 4
% 0.09/0.29 % launching worker at depth: 6
% 0.09/0.29 % launching worker at depth: 3
% 0.09/0.29 % launching worker at depth: 7
% 0.09/0.29 % launching worker at depth: 5
% 0.09/0.29 % launching worker at depth: 8
% 0.09/0.29 % launching worker at depth: 9
% 0.09/0.30 % launching worker at depth: 10
% 0.14/0.34 % launching worker at depth: 11
% 0.14/0.52 % launching worker at depth: 12
% 3.61/0.76 % SZS status Theorem for theBenchmark
% 3.61/0.76 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------