%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU324+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/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 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 9 unt; 0 def)
% Number of atoms : 132 ( 28 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 148 ( 54 ~; 52 |; 18 &)
% ( 1 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).
fof(involutiveness_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,subset_complement(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(dt_k3_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> element(subset_complement(X1,X2),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(t52_pre_topc,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( ( closed_subset(X2,X1)
=> topstr_closure(X1,X2) = X2 )
& ( ( topological_space(X1)
& topstr_closure(X1,X2) = X2 )
=> closed_subset(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_pre_topc) ).
fof(t55_tops_1,conjecture,
! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( top_str(X2)
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ! [X4] :
( element(X4,powerset(the_carrier(X2)))
=> ( ( open_subset(X4,X2)
=> interior(X2,X4) = X4 )
& ( interior(X1,X3) = X3
=> open_subset(X3,X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tops_1) ).
fof(t30_tops_1,axiom,
! [X1] :
( top_str(X1)
=> ! [X2] :
( element(X2,powerset(the_carrier(X1)))
=> ( open_subset(X2,X1)
<=> closed_subset(subset_complement(the_carrier(X1),X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tops_1) ).
fof(fc6_tops_1,axiom,
! [X1,X2] :
( ( topological_space(X1)
& top_str(X1)
& element(X2,powerset(the_carrier(X1))) )
=> open_subset(interior(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_tops_1) ).
fof(c_0_7,plain,
! [X46,X47] :
( ~ top_str(X46)
| ~ element(X47,powerset(the_carrier(X46)))
| interior(X46,X47) = subset_complement(the_carrier(X46),topstr_closure(X46,subset_complement(the_carrier(X46),X47))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tops_1])])]) ).
fof(c_0_8,plain,
! [X67,X68] :
( ~ element(X68,powerset(X67))
| subset_complement(X67,subset_complement(X67,X68)) = X68 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[involutiveness_k3_subset_1])]) ).
fof(c_0_9,plain,
! [X50,X51] :
( ~ element(X51,powerset(X50))
| element(subset_complement(X50,X51),powerset(X50)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k3_subset_1])]) ).
cnf(c_0_10,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]) ).
cnf(c_0_11,plain,
( subset_complement(X2,subset_complement(X2,X1)) = X1
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( element(subset_complement(X2,X1),powerset(X2))
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X80,X81] :
( ( ~ closed_subset(X81,X80)
| topstr_closure(X80,X81) = X81
| ~ element(X81,powerset(the_carrier(X80)))
| ~ top_str(X80) )
& ( ~ topological_space(X80)
| topstr_closure(X80,X81) != X81
| closed_subset(X81,X80)
| ~ element(X81,powerset(the_carrier(X80)))
| ~ top_str(X80) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t52_pre_topc])])])]) ).
cnf(c_0_14,plain,
( subset_complement(the_carrier(X1),topstr_closure(X1,X2)) = interior(X1,subset_complement(the_carrier(X1),X2))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_15,plain,
( topstr_closure(X2,X1) = X1
| ~ closed_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,negated_conjecture,
~ ! [X1] :
( ( topological_space(X1)
& top_str(X1) )
=> ! [X2] :
( top_str(X2)
=> ! [X3] :
( element(X3,powerset(the_carrier(X1)))
=> ! [X4] :
( element(X4,powerset(the_carrier(X2)))
=> ( ( open_subset(X4,X2)
=> interior(X2,X4) = X4 )
& ( interior(X1,X3) = X3
=> open_subset(X3,X1) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t55_tops_1]) ).
cnf(c_0_17,plain,
( interior(X1,subset_complement(the_carrier(X1),X2)) = subset_complement(the_carrier(X1),X2)
| ~ closed_subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_18,plain,
! [X76,X77] :
( ( ~ open_subset(X77,X76)
| closed_subset(subset_complement(the_carrier(X76),X77),X76)
| ~ element(X77,powerset(the_carrier(X76)))
| ~ top_str(X76) )
& ( ~ closed_subset(subset_complement(the_carrier(X76),X77),X76)
| open_subset(X77,X76)
| ~ element(X77,powerset(the_carrier(X76)))
| ~ top_str(X76) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t30_tops_1])])])]) ).
fof(c_0_19,plain,
! [X65,X66] :
( ~ topological_space(X65)
| ~ top_str(X65)
| ~ element(X66,powerset(the_carrier(X65)))
| open_subset(interior(X65,X66),X65) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc6_tops_1])]) ).
fof(c_0_20,negated_conjecture,
( topological_space(esk7_0)
& top_str(esk7_0)
& top_str(esk8_0)
& element(esk9_0,powerset(the_carrier(esk7_0)))
& element(esk10_0,powerset(the_carrier(esk8_0)))
& ( interior(esk7_0,esk9_0) = esk9_0
| open_subset(esk10_0,esk8_0) )
& ( ~ open_subset(esk9_0,esk7_0)
| open_subset(esk10_0,esk8_0) )
& ( interior(esk7_0,esk9_0) = esk9_0
| interior(esk8_0,esk10_0) != esk10_0 )
& ( ~ open_subset(esk9_0,esk7_0)
| interior(esk8_0,esk10_0) != esk10_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_21,plain,
( interior(X1,X2) = X2
| ~ closed_subset(subset_complement(the_carrier(X1),X2),X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_11]),c_0_12]) ).
cnf(c_0_22,plain,
( closed_subset(subset_complement(the_carrier(X2),X1),X2)
| ~ open_subset(X1,X2)
| ~ element(X1,powerset(the_carrier(X2)))
| ~ top_str(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( open_subset(interior(X1,X2),X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( interior(esk7_0,esk9_0) = esk9_0
| open_subset(esk10_0,esk8_0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,negated_conjecture,
topological_space(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
element(esk9_0,powerset(the_carrier(esk7_0))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,negated_conjecture,
top_str(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( open_subset(esk10_0,esk8_0)
| ~ open_subset(esk9_0,esk7_0) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( interior(esk7_0,esk9_0) = esk9_0
| interior(esk8_0,esk10_0) != esk10_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
( interior(X1,X2) = X2
| ~ open_subset(X2,X1)
| ~ element(X2,powerset(the_carrier(X1)))
| ~ top_str(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_31,negated_conjecture,
open_subset(esk10_0,esk8_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_26]),c_0_27])]),c_0_28]) ).
cnf(c_0_32,negated_conjecture,
element(esk10_0,powerset(the_carrier(esk8_0))),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,negated_conjecture,
top_str(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_34,negated_conjecture,
( ~ open_subset(esk9_0,esk7_0)
| interior(esk8_0,esk10_0) != esk10_0 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_35,negated_conjecture,
interior(esk7_0,esk9_0) = esk9_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_36,negated_conjecture,
~ open_subset(esk9_0,esk7_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_30]),c_0_31]),c_0_32]),c_0_33])]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_35]),c_0_25]),c_0_26]),c_0_27])]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU324+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n008.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:57:58 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.369s
%------------------------------------------------------------------------------