%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU323+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n008.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 : Tue May 5 05:11:29 PM UTC 2026
% Result : Theorem 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 5 unt; 0 def)
% Number of atoms : 83 ( 3 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 96 ( 39 ~; 36 |; 11 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 40 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc3_tops_1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& closed_subset(X2,X1)
& element(X2,powerset(the_carrier(X1))) )
=> open_subset(subset_complement(the_carrier(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_tops_1) ).
fof(d1_tops_1,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tops_1) ).
fof(fc2_tops_1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> closed_subset(topstr_closure(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_tops_1) ).
fof(dt_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(t51_tops_1,conjecture,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> open_subset(interior(X1,X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t51_tops_1) ).
fof(dt_k6_pre_topc,axiom,
! [X1,X2] :
( ( top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> element(topstr_closure(X1,X2),powerset(the_carrier(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_pre_topc) ).
fof(c_0_6,plain,
! [X34,X35] :
( ~ topological_space(X34)
| ~ top_str(X34)
| ~ closed_subset(X35,X34)
| ~ element(X35,powerset(the_carrier(X34)))
| open_subset(subset_complement(the_carrier(X34),X35),X34) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc3_tops_1])]) ).
fof(c_0_7,plain,
! [X60,X61] :
( ~ top_str(X60)
| ~ element(X61,powerset(the_carrier(X60)))
| interior(X60,X61) = subset_complement(the_carrier(X60),topstr_closure(X60,subset_complement(the_carrier(X60),X61))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tops_1])])]) ).
cnf(c_0_8,plain,
( open_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ closed_subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( interior(X1,X2) = subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X2)))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X46,X47] :
( ~ topological_space(X46)
| ~ top_str(X46)
| ~ element(X47,powerset(the_carrier(X46)))
| closed_subset(topstr_closure(X46,X47),X46) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_tops_1])]) ).
fof(c_0_11,plain,
! [X42,X43] :
( ~ element(X43,powerset(X42))
| element(subset_complement(X42,X43),powerset(X42)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> open_subset(interior(X1,X2),X1) ) ),
inference(assume_negation,[status(cth)],[t51_tops_1]) ).
cnf(c_0_13,plain,
( open_subset(interior(X1,X2),X1)
| ~ element(topstr_closure(X1,subset_complement(the_carrier(X1),X2)),powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ closed_subset(topstr_closure(X1,subset_complement(the_carrier(X1),X2)),X1)
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
( closed_subset(topstr_closure(X1,X2),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
( element(subset_complement(X2,X1),powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X44,X45] :
( ~ top_str(X44)
| ~ element(X45,powerset(the_carrier(X44)))
| element(topstr_closure(X44,X45),powerset(the_carrier(X44))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k6_pre_topc])]) ).
fof(c_0_17,negated_conjecture,
( topological_space(esk6_0)
& top_str(esk6_0)
& element(esk7_0,powerset(the_carrier(esk6_0)))
& ~ open_subset(interior(esk6_0,esk7_0),esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_18,plain,
( open_subset(interior(X1,X2),X1)
| ~ element(topstr_closure(X1,subset_complement(the_carrier(X1),X2)),powerset(the_carrier(X1)))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_19,plain,
( element(topstr_closure(X1,X2),powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
~ open_subset(interior(esk6_0,esk7_0),esk6_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( open_subset(interior(X1,X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1)
| ~ topological_space(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15]) ).
cnf(c_0_22,negated_conjecture,
element(esk7_0,powerset(the_carrier(esk6_0))),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
top_str(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,negated_conjecture,
topological_space(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU323+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n008.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:57:28 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------